Polyhedron stubs

In the context of Wikipedia and other online collaborative projects, "polyhedron stubs" refer to short or incomplete articles that provide minimal information about polyhedra, which are three-dimensional geometric shapes with flat faces, straight edges, and vertices. A stub is essentially a starting point for more comprehensive articles, and it marks content that needs expansion and additional detail.

An apeirogonal antiprism is a type of geometric figure that belongs to the family of antiprisms, which are polyhedra formed by two parallel bases connected by triangular faces. In the case of an apeirogonal antiprism, the bases are apeirogons, which are polygons with an infinite number of sides.

An apeirogonal prism is a type of geometric figure that extends the concept of a prism to an infinite number of sides. Specifically, an apeirogon is a polygon with an infinite number of sides. Therefore, an apeirogonal prism consists of two parallel apeirogons (one serving as the base and the other as the top) connected by a series of vertical edges or faces.

The augmented dodecahedron is a type of Archimedean solid that can be described as an augmentation of the regular dodecahedron. In geometry, augmentation refers to a process where faces of a polyhedron are modified by adding new faces.

An augmented hexagonal prism is a geometric figure that is based on the structure of a standard hexagonal prism but modified by adding additional features or shapes. ### Basic Structure: 1. **Hexagonal Prism**: The standard hexagonal prism consists of two hexagonal bases connected by six rectangular lateral faces. The height of the prism is defined as the distance between the two hexagonal bases.

An augmented pentagonal prism is a type of polyhedron that is created by taking a standard pentagonal prism and adding a pyramid (or cone) on one or both of its hexagonal faces. Here are some details about the augmented pentagonal prism: - **Base Shapes**: The base of the prism consists of two pentagons, which are parallel to each other, and the sides are made up of five rectangular faces.

An "augmented sphenocorona" is a type of geometric figure that belongs to the category of polyhedra. Specifically, it is a variant of the sphenocorona—one of the Archimedean solids. The term "augmented" indicates that some vertices or faces have been altered or added to the original sphenocorona to create a new shape. A sphenocorona itself is characterized by having a combination of triangular and quadrilateral faces.

An augmented triangular prism is a three-dimensional geometric shape that is created by adding a pyramid-like structure (often referred to as an "augmentation") to one of the triangular faces of a triangular prism. A triangular prism itself consists of two parallel triangular bases connected by three rectangular lateral faces. When you augment one of the triangular bases, you typically create a new face that extends out from the base, adding volume and complexity to the shape.

An augmented tridiminished icosahedron is a type of polyhedron that is derived from the tridiminished icosahedron through a process called augmentation. To understand this concept, it's helpful to break down the terms involved: 1. **Icosahedron**: A regular polyhedron with 20 equilateral triangular faces, 30 edges, and 12 vertices.

The Augmented Truncated Cube is a convex polyhedron that is categorized as an Archimedean solid. It is formed by augmenting the truncated cube, which itself is derived from truncating the corners of a cube, thereby creating additional polygonal faces. ### Description: - The Augmented Truncated Cube can be visualized as follows: - Start with a cube. - Truncate (cut off) its vertices, resulting in a truncated cube that has additional triangular faces.

The augmented truncated dodecahedron is a type of Archimedean solid. It can be described as an extension of the truncated dodecahedron by adding a pyramid (or a cone) to each of its faces. Here are some key characteristics of the augmented truncated dodecahedron: 1. **Vertices**: It has 60 vertices. 2. **Edges**: There are 120 edges.

An augmented truncated tetrahedron is a type of polyhedron formed by augmenting a truncated tetrahedron. ### Truncated Tetrahedron First, let's understand the truncated tetrahedron. It is one of the Archimedean solids and can be obtained by slicing the vertices of a regular tetrahedron. The result has: - 4 triangular faces, - 4 hexagonal faces, - 12 edges, and - 8 vertices.

A biaugmented pentagonal prism is a type of polyhedron that can be categorized as a member of the family of augmented prisms. It is constructed from a standard pentagonal prism by adding two additional pentagonal pyramids (the "augmentation") at both of its pentagonal bases. ### Characteristics of a Biaugmented Pentagonal Prism: 1. **Faces**: The biaugmented pentagonal prism has a total of 12 faces.

A biaugmented triangular prism is a type of geometrical solid that is classified as a polyhedron. It is a modification of the triangular prism, which itself consists of two triangular bases and three rectangular lateral faces. In a biaugmented triangular prism, two additional triangular faces (the augmentations) are added to the two triangular bases of the prism.

The biaugmented truncated cube is a type of Archimedean solid, which is a class of convex polyhedra with regular polygons as their faces and identical vertices. The biaugmented truncated cube can be derived from the truncated cube by augmenting it with additional pyramidal structures (or "augments") at two opposing square faces. Here are some details about the biaugmented truncated cube: - **Vertices**: The solid has 24 vertices.

A bifrustum is a geometric shape that can be considered as a variant of a frustum. Specifically, it is formed by taking two frustums of identical cross-sectional shapes and placing them back to back. Each half of a bifrustum resembles a frustum, which is the portion of a solid (typically a cone or pyramid) that lies between two parallel planes.

The bigyrate diminished rhombicosidodecahedron is a complex geometric figure that belongs to the category of Archimedean solids. It is constructed through the process of truncating or diminishing the faces of the rhombicosidodecahedron, one of the five Platonic solids.

Cantellation is a geometric operation that involves the modification of a polyhedron or polytope by truncating its vertices. When you cantell a polyhedron, you effectively "cut off" its vertices, creating new faces that replace the original vertices with additional edges, typically forming a structure that combines aspects of the original shape and its modified version. The result of cantellation can create more complex shapes with additional faces while preserving some of the properties of the original polyhedron.

The compound of a cube and an octahedron typically refers to a geometric configuration where both shapes are interlinked in a specific way. A well-known example of such a compound is the "cuboctahedron." However, the term can also describe the arrangement known as the "cube-octahedron compound," which features both the cube and octahedron sharing the same center, with their vertices and faces interleaved.

A compound of eight octahedra with rotational freedom refers to a geometric arrangement where eight octahedral shapes are combined in a way that allows for rotational movement around their connecting points or edges. In geometry, an octahedron is a polyhedron with eight triangular faces, 12 edges, and 6 vertices. When creating a compound of octahedra, they can be arranged to share vertices, edges, or face connections, resulting in a complex three-dimensional structure.

A compound of eight triangular prisms refers to a three-dimensional geometric figure formed by combining eight individual triangular prisms in a specific arrangement. Triangular prisms have two triangular bases and three rectangular faces connecting the bases. When creating a compound of these prisms, they can be arranged in various configurations, such as adjacent to each other, stacked, or rotated in different orientations. The exact appearance and properties of the compound will depend on how the prisms are arranged.

The "compound of five cubes" refers to a specific geometric arrangement in three-dimensional space. It is a polyhedral structure made by combining five identical cubes in such a way that they share certain faces and vertices. Visualizing the compound, it consists of a central cube with four additional cubes attached to its faces (typically one on each face of the central cube). This arrangement creates a more complex solid that can have interesting geometric properties and symmetry.

The compound of five cuboctahedra is a geometric structure that consists of five cuboctahedra arranged in a specific way. The cuboctahedron is a convex Archimedean solid that has 8 triangular faces and 6 square faces, with 12 edges and 12 vertices. In the context of a compound, the term typically refers to a geometric arrangement where multiple polyhedra share some points or overlap in a way that creates an intricate three-dimensional figure.

The compound of five cubohemioctahedra is a three-dimensional geometric structure that consists of five cubohemioctahedra arranged in a symmetrical configuration. A cubohemioctahedron itself is a convex Archimedean solid, which can be described as having both cube and octahedron characteristics. In this compound, the cubohemioctahedra intersect and share vertices and faces, creating a complex arrangement that showcases the beauty of polyhedral symmetry.

The compound of five great cubicuboctahedra is a complex geometric structure formed by the intersection of five great cubicuboctahedra, which are Archimedean solids characterized by their combination of squares and octagons in their faces. In geometry, a compound involves two or more polyhedra that intersect in a symmetrical way. The great cubicuboctahedron itself is a convex polyhedron featuring 8 triangular faces, 24 square faces, and symmetrical properties.

The "Compound of five great dodecahedra" is a fascinating geometric structure composed of five great dodecahedra (a type of polyhedron with twelve regular pentagonal faces) arranged in a symmetrical way. Each great dodecahedron is a member of the family of structures known as Archimedean solids, and specifically, it is one of the duals of the icosahedron.

The "Compound of Five Great Icosahedra" is a fascinating geometric structure in the realm of polyhedra. It is formed by arranging five great icosahedra (the dual polyhedron of the dodecahedron) around a common center. ### Characteristics: - **Vertices**: The compound has a unique vertex arrangement due to the overlapping and symmetry of the five great icosahedra.

A compound of five great rhombihexahedra consists of five instances of the great rhombihexahedron, a type of convex polyhedron that is a member of the Archimedean solids. The great rhombihexahedron is composed of hexagonal and square faces. In geometric terms, the compound of these five great rhombihexahedra involves arranging them in such a way that they interpenetrate each other.

A compound of five icosahedra refers to a geometric arrangement where five icosahedra (which are polyhedra with 20 triangular faces, 12 vertices, and 30 edges) are combined in a specific way to form a new polyhedral structure. This kind of arrangement is often explored in the context of geometric studies such as polyhedral compounds, where multiple identical polyhedra are intersected or arranged around a common center.

The compound of five nonconvex great rhombicuboctahedra is a fascinating arrangement in the field of geometry, specifically in the study of polyhedra and their combinations. The great rhombicuboctahedron is a nonconvex Archimedean solid, composed of 8 square and 24 triangular faces, and has some interesting properties related to symmetry and vertex arrangement.

The compound of five octahedra, also known as the "pentaoctahedron," is a geometric structure formed by combining five octahedra in a specific arrangement. It can be viewed as a complex polyhedron or a space-filling arrangement. In polyhedral geometry, such compounds often demonstrate interesting symmetrical properties and can be visualized in three-dimensional space.

The compound of five octahemioctahedra is a geometric arrangement that involves five octahemioctahedra, a type of polyhedron. The octahemioctahedron is a non-convex uniform polyhedron that has 16 faces: 8 triangles and 8 hexagons.

The compound of five rhombicuboctahedra is a complex geometric figure created by arranging five rhombicuboctahedra (a type of Archimedean solid) in a specific spatial configuration. A rhombicuboctahedron itself is a convex polyhedron with 26 faces (8 triangular faces and 18 square faces), and it features 24 edges and 12 vertices.

A compound of five small cubicuboctahedra is a geometric shape formed by combining five small cubicuboctahedra in a specific arrangement. A cubicuboctahedron is a polyhedron with 8 triangular faces and 6 square faces, characterized as an Archimedean solid. In this compound, the five cubicuboctahedra would be positioned in such a way that they share vertices and/or edges but maintain their individual geometric properties.

The compound of five small rhombihexahedra is a complex geometric arrangement that consists of five small rhombihexahedra, which are dual to the cuboctahedron. Each rhombihexahedron is a polyhedron with 12 faces (6 rhombic and 6 square), and when combined in this compound, they create an intricate mathematical structure.

The compound of five small stellated dodecahedra is a fascinating geometric configuration in the field of polyhedral studies. In this arrangement, five small stellated dodecahedra, which are star-shaped polyhedra (or stellations) derived from the regular dodecahedron, are combined in a symmetrical way.

The compound of five stellated truncated hexahedra is a complex geometric arrangement that combines five instances of a stellated truncated hexahedron. A stellated truncated hexahedron is a polyhedron derived from a truncated cube by stellating its faces, resulting in a shape that has a more intricate structure with additional points or "spikes.

The compound of five tetrahemihexahedra is a fascinating geometric structure involving five tetrahemihexahedra arranged in a symmetrical formation. The tetrahemihexahedron itself is a type of Archimedean solid characterized by its unique combination of triangular and square faces. Specifically, it consists of 8 triangular faces and 6 square faces.

The compound of five truncated cubes is a geometric figure made up of five truncated cubes arranged in a specific way. A truncated cube is formed by truncating (cutting off) the corners of a cube, resulting in a solid with 8 regular hexagonal faces and 6 square faces. When five such truncated cubes are combined, they form a complex structure that is part of the family of polyhedra.

The compound of five truncated tetrahedra is a three-dimensional geometric structure formed by placing five truncated tetrahedra such that they intersect in a specific way. A truncated tetrahedron is created by truncating (slicing off) the vertices of a regular tetrahedron, resulting in a polyhedron that has 4 triangular faces and 4 hexagonal faces.

The term "compound of four cubes" refers to a three-dimensional geometric shape constructed by combining four individual cubes in a specific arrangement. This shape can be visualized as each of the four cubes sharing faces with the others, creating a single cohesive structure. One common arrangement for the compound of four cubes is to place the cubes so that they form the shape of a larger cube (specifically, a 2x2x2 cube) when viewed from a certain angle.

The compound of four hexagonal prisms refers to a geometric arrangement where four hexagonal prism shapes are combined or arranged together in some manner. In geometry, a hexagonal prism is a three-dimensional solid with two parallel hexagonal bases and six rectangular sides connecting the bases.

The compound of four octahedra is a geometric arrangement or polyhedral compound formed by combining four octahedra in a specific way. When arranged symmetrically, these octahedra can interpenetrate each other, creating a complex shape that often highlights the symmetrical and aesthetic properties of polyhedra. In three-dimensional space, an octahedron is a shape with eight faces, each of which is an equilateral triangle.

The compound of four octahedra with rotational freedom refers to a specific geometric arrangement where four octahedra are combined in a way that they can rotate freely relative to each other. An octahedron is a polyhedron with eight triangular faces, and combining multiple octahedra can create interesting structures. In the context of mathematical or geometric studies, such compounds can exhibit symmetry and complex spatial relationships.

A compound of four triangular prisms refers to a solid formed by combining four triangular prisms in some way. In geometry, a triangular prism is a three-dimensional shape with two parallel triangular bases and three rectangular faces connecting corresponding sides of the triangles. When talking about a compound of four triangular prisms, it could mean different configurations: 1. **Aligned Arrangement**: The four prisms might be arranged in a straight line, sharing a common face or edge.

The compound of the great icosahedron and the great stellated dodecahedron is known as the "stella octangula" or "octahedral compound." This compound is a three-dimensional figure formed by the intersection of two polyhedra: a great icosahedron (which is one of the Archimedean solids) and a great stellated dodecahedron (a star polyhedron).

The term "compound of six cubes" generally refers to a geometric configuration where six individual cubes are arranged together in a specific way. One notable example of this is the "compound of six cubes" in three-dimensional space, which can illustrate interesting properties of geometry and space-filling.

The concept of "Compound of six cubes with rotational freedom" generally refers to a geometric arrangement where six cubes are combined in a specific way, allowing for rotational transformations. This type of structure is often discussed in the context of three-dimensional geometry and can pertain to various fields, including mathematics, art, and architecture.

A compound of six decagonal prisms refers to a three-dimensional shape formed by the arrangement of six decagonal prisms combined into one entity. A **decagonal prism** is a type of prism that has two decagonal (10-sided) bases connected by rectangular faces. In this compound, six such prisms are placed together in a specific configuration.

The compound of six decagrammic prisms refers to a specific geometric arrangement formed by combining six decagrammic prisms, which are three-dimensional shapes with a decagram (10-sided polygon) as their bases. Each decagrammic prism has two parallel faces that are decagrams and rectangular lateral faces connecting corresponding sides of the two bases. When these six prisms are combined in a specific manner, they can form a three-dimensional structure.

The compound of six octahedra is a geometric arrangement consisting of six regular octahedra arranged in such a way that they share some of their faces, vertices, or edges. One notable example is the "octahedral group," which represents the symmetry of the octahedron and can show how multiple octahedra can be combined in space.

The compound of six pentagonal prisms is a fascinating geometric arrangement consisting of six individual pentagonal prisms that are arranged in a specific way. Each pentagonal prism is a three-dimensional shape with two pentagonal bases and five rectangular lateral faces. When six of these prisms are combined into a single geometric compound, they typically share edges and vertices, creating a more complex shape.

A compound of six pentagrammic prisms refers to a polyhedral structure formed by combining six pentagrammic prisms. A pentagrammic prism itself is a three-dimensional geometric shape that has two pentagram (five-pointed star) bases connected by rectangular lateral faces. When multiple pentagrammic prisms are combined into a compound, they share spatial relationships and may intersect or connect in various ways.

The compound of six tetrahedra is a geometric structure formed by the combination of six tetrahedra intersecting in a symmetric arrangement. In this compound, the tetrahedra are arranged in such a way that they share vertices, edges, and faces, creating a complex polyhedral configuration. This compound can also be described mathematically as a polyhedral arrangement with an intricate symmetry. It is an interesting example of a polyhedral compound in three-dimensional space and showcases the fascinating interplay between geometry and symmetry.

The "compound of six tetrahedra" refers to a specific geometric arrangement of six tetrahedra that share a common center but can rotate freely. This structure can be visualized as a three-dimensional arrangement where pairs of tetrahedra are arranged around a central point, often showcasing the symmetrical properties of both tetrahedra and the overall compound.

The compound of the small stellated dodecahedron and the great dodecahedron is a fascinating geometric arrangement that combines two polyhedra. 1. **Small Stellated Dodecahedron**: This is a non-convex polyhedron formed by extending the faces of a regular dodecahedron. It has 12 star-shaped faces (which are actually pentagrams) and possesses 20 vertices and 30 edges.

A compound of ten hexagonal prisms would refer to a geometric figure constructed by joining ten individual hexagonal prisms together in some manner. A hexagonal prism is a three-dimensional shape with two hexagonal bases connected by six rectangular faces. To form a compound with ten of these prisms, they could be arranged in various configurations, such as: 1. Stacked vertically, where the hexagonal prisms are aligned on top of each other.

The term "compound of ten octahedra" typically refers to a geometric arrangement or a polyhedral combination involving ten octahedra. In geometry, a compound is a three-dimensional shape formed from two or more shapes that coexist in a specific spatial arrangement. One common example of a compound of octahedra is the arrangement known as the "octahedral compound," which consists of two interpenetrating octahedra.

The compound of ten tetrahedra is a three-dimensional geometric figure that is formed by intersecting ten tetrahedra in a specific arrangement. When combined in this way, the resulting structure exhibits fascinating symmetry and complexity. In this compound, each of the ten tetrahedra shares vertices with others, and they are often arranged so that they occupy a central region corresponding to their geometric properties, displaying rich visual patterns.

A compound of ten triangular prisms would consist of ten distinct triangular prisms arranged in a specific geometric configuration. Triangular prisms themselves are three-dimensional shapes with two triangular bases and three rectangular sides. When discussing a compound of these prisms, it may refer to several arrangements, such as: 1. **Separated:** The prisms are placed apart from each other in space without intersecting.

A compound of ten truncated tetrahedra is a three-dimensional geometric arrangement made up of ten truncated tetrahedron shapes. A truncated tetrahedron is a type of polyhedron created by truncating (slicing off) the vertices of a regular tetrahedron. This action results in a geometric figure that has 4 triangular faces and 4 hexagonal faces. In this particular compound, the ten truncated tetrahedra are arranged in such a way that they intersect with one another, forming a symmetrical structure.

The term "compound of three tetrahedra" refers to a specific geometric configuration in three-dimensional space. In this context, it typically describes a compound polyhedron composed of three tetrahedra that are arranged in such a way that they share certain vertices and edges. One common way to visualize this compound is through the arrangement where the three tetrahedra are positioned with their vertices meeting at a central point, creating a complex shape.

The compound of twelve pentagonal antiprisms with rotational freedom refers to a complex geometric structure that consists of twelve pentagonal antiprisms arranged in a way that allows for rotational movement. A pentagonal antiprism is a polyhedron with two parallel pentagonal bases and ten triangular lateral faces. In this compound, each antiprism can rotate around its central axis, creating a dynamic interaction between the antiprisms.

A compound of twelve pentagonal prisms refers to a geometric figure formed by arranging twelve pentagonal prisms in a specific way. In three-dimensional geometry, a pentagonal prism is a polyhedron with two parallel pentagonal bases connected by rectangular faces. When we talk about a compound of twelve pentagonal prisms, this can imply various configurations depending on how the prisms are arranged or combined.

The "Compound of twelve pentagrammic prisms" is a geometrical figure that consists of twelve pentagrammic prisms arranged in a specific manner. A pentagrammic prism is a three-dimensional shape formed by extending a pentagram (a five-pointed star) along a perpendicular axis, effectively creating a prism with a pentagram as its base.

The "Compound of twelve tetrahedra" is a geometric structure composed of twelve tetrahedra arranged in such a way that they intersect and share vertices, edges, and faces, creating a complex arrangement. This compound is notable for its symmetric properties and rotational freedom, meaning that it can be rotated around certain axes while maintaining its overall shape.

The compound of twenty octahedra is a geometric arrangement made up of 20 individual octahedral shapes. In a three-dimensional space, an octahedron is a polyhedron with eight faces, which are all equilateral triangles. When multiple octahedra are combined, they can create intricate structures. The compound of twenty octahedra often refers to a specific geometric construction where these octahedra are arranged in a symmetrical way.

The term "compound of twenty octahedra with rotational freedom" is likely referring to a specific geometric structure or arrangement involving multiple octahedra. In geometry, a **compound** often refers to a three-dimensional shape formed by combining multiple identical shapes. One way to interpret "twenty octahedra" is that it may refer to a compound constructed from twenty individual octahedral shapes.

The compound of twenty tetrahemihexahedra is a specific arrangement of geometric shapes in three-dimensional space. The tetrahemihexahedron, which is also known as the truncated tetrahedron, can be understood as a polyhedron with specific properties. A tetrahemihexahedron has 6 faces (each being a triangle), 12 edges, and 4 vertices. It is created by truncating the vertices of a regular tetrahedron.

A compound of twenty triangular prisms would be a three-dimensional geometric figure composed of twenty individual triangular prisms combined in some way. A triangular prism itself consists of two triangular bases and three rectangular lateral faces. To create a compound of twenty triangular prisms, you can arrange or connect these prisms in various configurations. The specific arrangement and properties of the compound would depend on how the prisms are oriented and connected.

The compound of two great dodecahedra is a three-dimensional geometric arrangement in which two great dodecahedra are combined in such a way that they intersect each other. A great dodecahedron is a type of regular polyhedron that is made up of 12 regular pentagonal faces, and it is one of the Archimedean solids. When two great dodecahedra are combined, they can create a fascinating and complex structure.

The compound of two great icosahedra is a geometric figure formed by the intersection and arrangement of two great icosahedra in space. A great icosahedron is a type of polyhedron that is a dual of the standard (or regular) icosahedron. It can be visualized as a star-shaped figure with multiple vertices. When two great icosahedra are combined, their vertices and faces intersect in a symmetrical manner, creating a complex geometric structure.

The compound of two great inverted snub icosidodecahedra is a geometric structure formed by the intersection of two great inverted snub icosidodecahedra. To break it down: - **Great inverted snub icosidodecahedron** is a convex Archimedean solid that combines the features of an icosidodecahedron and has a "snub" characteristic.

The compound of two great retrosnub icosidodecahedra is a complex geometric figure that results from the combination of two mathematically defined shapes known as the great retrosnub icosidodecahedra. First, let's break down the components: 1. **Great Retrosnub Icosidodecahedron**: This is a Archimedean solid, which is a type of convex polyhedron with identical vertices and faces that are regular polygons.

The compound of two great snub icosidodecahedra is a geometric figure that consists of two instances of the great snub icosidodecahedron interpenetrating each other. The great snub icosidodecahedron is a nonconvex Archimedean solid with 92 faces (12 regular pentagons and 80 equilateral triangles), 150 edges, and 60 vertices.

The compound of two icosahedra is a geometric configuration formed by the intersection of two icosahedra. An icosahedron is a polyhedron with 20 triangular faces, and when two of them are combined, they can create a visually complex shape. In this specific compound, one icosahedron is typically inverted and placed within another. The resulting structure is symmetric and exhibits interesting geometric properties.

The term "compound of two inverted snub dodecadodecahedra" refers to a specific geometric arrangement involving two snub dodecadodecahedra (also known as snub icosidodecahedra or snub dodecahedra) that are positioned in such a way that one is inverted relative to the other.

The compound of two small stellated dodecahedra is a geometric figure formed by the combination of two small stellated dodecahedra, which are both stellated versions of the dodecahedron. The small stellated dodecahedron is a convex polyhedron made up of 12 star-shaped faces, each a pentagram.

The compound of two snub cubes is a fascinating geometrical structure that arises from the combination of two snub cubes, which are Archimedean solids. A snub cube has 38 faces: 6 square faces and 32 triangular faces, and it can be constructed by taking a cube, truncating its corners, and then performing a process called snubbing.

The compound of two snub dodecadodecahedra is a fascinating geometric figure composed of two identical snub dodecadodecahedra that are interlaced with each other. A snub dodecadodecahedron is one of the Archimedean solids, characterized by its mixture of dodecahedral and triangular faces. It has 12 regular pentagonal faces and 20 equivalent triangular faces.

The compound of two snub dodecahedra is a geometric structure formed by the intersection of two snub dodecahedra. A snub dodecahedron is a convex Archimedean solid with 12 regular pentagonal faces and 20 triangular faces, featuring a distinct and non-uniform arrangement of vertices and edges. When two snub dodecahedra are combined, they can be positioned in such a way that they intersect.

The compound of two snub icosidodecadodecahedra is a complex geometric structure formed by the combination of two snub icosidodecadodecahedra. A snub icosidodecadodecahedron itself is a convex Archimedean solid with a specific arrangement of faces, including triangles and pentagons. When two of these solids are combined, they intersect in a way that can create a visually interesting and intricate structure.

The compound of two truncated tetrahedra forms a polyhedral structure that is intriguing in both geometry and topology. A truncated tetrahedron, which is one of the Archimedean solids, is created by truncating (slicing off) the corners (vertices) of a regular tetrahedron, resulting in a solid with 4 triangular faces and 4 hexagonal faces.

The cubitruncated cuboctahedron is a type of Archimedean solid, which is a convex polyhedron with regular polygonal faces and identical vertices. More specifically, it is derived from the cuboctahedron through a process known as truncation.

The cubohemioctahedron is a type of convex polyhedron that belongs to the category of Archimedean solids. It is defined by its unique geometric properties: it has 8 triangular faces, 6 square faces, and 12 vertices, with each vertex being a meeting point for 3 square faces and 1 triangular face.

A decagonal antiprism is a type of polyhedron and a specific case of an antiprism. It is formed by two parallel decagonal (10-sided) polygons, one positioned directly above the other, and connected by a series of triangular faces.

A decagonal bipyramid is a type of three-dimensional geometric shape that belongs to the family of polyhedra. Specifically, it is a bipyramid based on a decagon, which is a polygon with ten sides. ### Characteristics of a Decagonal Bipyramid: 1. **Base Faces**: The decagonal bipyramid has two decagonal faces as its bases, one at the top and one at the bottom.

A decagonal prism is a three-dimensional geometric shape that has two parallel bases in the shape of a decagon (a polygon with ten sides) and rectangular sides connecting the corresponding sides of the two bases. Key characteristics of a decagonal prism include: 1. **Bases**: The top and bottom faces are both decagons. 2. **Faces**: In addition to the two decagonal bases, the prism has ten rectangular lateral faces.

A decagrammic antiprism is a type of polyhedron that belongs to the family of antiprisms. Specifically, it is formed by connecting two decagrams (10-sided star polygons) with a band of quadrilateral faces that are typically parallelograms. In more detail: - **Decagram**: A star polygon with 10 vertices, which can be visualized as a ten-pointed star.

A decagrammic prism is a type of polyhedron characterized by its decagrammic base and straight, vertical sides. 1. **Base Shape**: The term "decagrammic" refers to a 10-sided star polygon, often constructed by connecting every second vertex of a regular decagon (10-sided polygon).

The deltoidal hexecontahedron is a convex Archimedean solid characterized by its unique geometrical properties. Specifically, it has 60 faces, all of which are deltoids (a type of kite-shaped quadrilateral). The solid features 120 edges and 60 vertices.

A diminished rhombic dodecahedron is a polyhedral shape that is derived from the regular rhombic dodecahedron by truncating its vertices. Essentially, this process involves slicing off the corners of the rhombic dodecahedron, which results in a new figure with more faces.

Disphenocingulum is a genus of extinct reptiles that belonged to the group known as parareptiles. These creatures are characterized by their unique skull structure and dental patterns. Disphenocingulum lived during the late Permian period, which was around 260 million years ago. Fossils of Disphenocingulum have been found, providing insights into the diversity of early reptiles and their evolutionary history.

The ditrigonal dodecadodecahedron is a convex Archimedean solid, which is notable for its unique geometry. It is characterized by having 12 faces that are each ditrigonal triangles, combined with 20 faces that are regular pentagons. This polyhedron has a total of 60 edges and 20 vertices.

A dodecagonal prism is a three-dimensional geometric shape that consists of two parallel faces that are regular dodecagons (12-sided polygons) and additional rectangular faces connecting the corresponding edges of the dodecagons. Key characteristics of a dodecagonal prism include: 1. **Base Faces**: The two bases are regular dodecagons, meaning all sides are of equal length and all interior angles are equal (each angle measures 150 degrees).

An elongated bicupola is a type of Archimedean solid, which is a polyhedron made up of two identical cupolae (which are dome-like structures) connected by a cylindrical section. It can be visualized as taking two cupolae (specifically, a square cupola or a triangular cupola) and joining them together, but with an elongated shape.

An elongated bipyramid is a type of convex polyhedron that can be classified as a member of the family of bipyramids. It is formed by taking a regular polygon and adding two additional vertices that are positioned along the axis perpendicular to the polygon's plane. This elongates the resulting bipyramid compared to a standard bipyramid, which has two identical bases and equally spaced apex points above and below the center of the base.

An elongated cupola is a polyhedral structure that combines the features of a cupola and a prism. In geometry, a cupola is typically formed by taking a polygon and connecting its vertices to a single point above the polygon (the apex), resulting in a structure with a base that is a polygon and lateral faces that are triangles. In the case of an elongated cupola, the basic structure is elongated by adding an additional layer of polygonal faces at the top.

An elongated hexagonal bipyramid is a type of polyhedron that is part of the family of bipyramids. It is specifically derived from a hexagonal bipyramid by elongating it along its axis. ### Structure: - **Base Faces**: The elongated hexagonal bipyramid has two hexagonal bases connected by triangular faces. The primary difference from a regular hexagonal bipyramid is the elongation, which typically results in a pair of additional faces being introduced.

The elongated pentagonal bipyramid is a type of geometric solid that belongs to the category of polyhedra. It can be described as a bipyramid based on a pentagonal base, with one additional pyramid added to one of its vertices, extending the geometry. ### Characteristics: - **Faces**: The elongated pentagonal bipyramid has 12 faces in total: 5 of the faces are hexagons (from the two base pentagons being connected) and 7 faces are triangles.

The elongated pentagonal cupola is a type of convex polyhedron and a member of the Archimedean solids. Specifically, it is formed by elongating a pentagonal cupola through the addition of two hexagonal faces on opposite sides.