The elongated pentagonal gyrobirotunda is a type of convex polyhedral compound classified within the broader category of Archimedean solids. It belongs to a group of shapes known as the gyrobirotunda, which are characterized by their symmetrical arrangement of pentagonal and triangular faces. Here are some key characteristics of the elongated pentagonal gyrobirotunda: 1. **Faces**: This solid has a combination of faces, specifically including pentagons and triangles.

The great triakis octahedron is a type of Archimedean solid, which is a category of convex polyhedra characterized by having regular polygonal faces and uniform vertex arrangements. Specifically, the great triakis octahedron can be described as follows: 1. **Face Composition**: It consists of 24 equilateral triangular faces and 8 regular quadrilateral faces. The triangular faces are arranged around the edges of the octahedral structure.

A Noble polyhedron is a type of convex polyhedron that possesses a high degree of symmetry and a well-known set of properties. Specifically, they are characterized by having regular polygons as their faces and being derived from regular polyhedra through certain symmetrical operations. Noble polyhedra are defined by their dual relationships with regular and semi-regular polyhedra, exhibiting uniformity in the arrangement of their vertices, edges, and faces.

An octagonal bipyramid is a type of polyhedron that is classified within the category of bipyramids. It is formed by connecting two identical octagonal bases at their corresponding vertices.

The term "parabiaugmented truncated dodecahedron" refers to a specific type of geometric shape, which belongs to the family of Archimedean solids. To break it down: 1. **Dodecahedron**: The regular dodecahedron is a polyhedron composed of 12 regular pentagonal faces, 20 vertices, and 30 edges.

A pentagonal antiprism is a type of geometric solid that belongs to a family known as antiprisms. It is constructed by taking two pentagonal bases that are parallel to each other and connected by a series of triangular faces. The triangular faces are arranged around the sides of the bases and are oriented such that they provide a twist between the two bases.

A rhombic icosahedron is a type of polyhedron that has 20 faces, with each face being a rhombus. It is a member of the class of Archimedean solids and is characterized by its symmetrical shape and uniform vertex configuration. Here are some key features of the rhombic icosahedron: 1. **Faces**: It has 20 rhombic faces.

A pentagrammic prism is a type of three-dimensional geometric figure (a polyhedron) that consists of two parallel pentagrammic bases connected by rectangular sides. Here’s a breakdown of the components: 1. **Pentagram**: A pentagram is a five-pointed star formed by extending the sides of a regular pentagon. It has five vertices and five edges, and it can be drawn continuously without lifting the pen.

A rectified truncated dodecahedron is a geometric shape that is part of the family of Archimedean solids. It is derived from the dodecahedron through a process of truncation (cutting off the vertices) and rectification (the process of replacing faces with vertices or edges).

A rectified truncated tetrahedron is a geometric shape that results from the modification of a regular tetrahedron through two operations: truncation and rectification. 1. **Truncation**: This process involves cutting off the vertices of the tetrahedron. When you truncate a tetrahedron, you replace each of its four vertices with a new face (which, for a tetrahedron, will be a triangle). This operation creates additional edges and faces in the shape.

The small rhombidodecacron is a type of convex polyhedron that belongs to the family of Archimedean solids. Specifically, it is a uniform polyhedron characterized by its unique arrangement of faces, vertices, and edges. ### Properties of Small Rhombidodecacron: 1. **Faces**: It has 62 faces in total, comprising 12 regular pentagons and 50 rhombuses. 2. **Vertices**: It has 30 vertices.

A small hexagonal hexecontahedron is a polyhedron that is classified as a member of the family of convex polyhedra. Specifically, it is a type of Archimedean solid. The term "hexecontahedron" indicates that it has 60 faces. In the case of the small hexagonal hexecontahedron, these faces include hexagons and other polygons.

The snub square antiprism is a type of Archimedean solid, which is a convex polyhedron that has identical vertices and faces that are regular polygons. Specifically, the snub square antiprism can be described as a modification of the square antiprism. It has the following characteristics: - **Faces**: The snub square antiprism has 38 faces in total, consisting of 8 triangles and 30 squares.

A square orthobicupola is a type of polyhedron that belongs to the category of Archimedean solids. Specifically, it is formed by the combination of two square cupolas and has a unique geometric configuration. ### Features of the Square Orthobicupola: 1. **Faces**: The square orthobicupola has a total of 24 faces. These consist of: - 8 square faces - 16 triangular faces 2.

A triangular bifrustum is a three-dimensional geometric shape that is essentially formed by truncating the top and bottom of a triangular prism. Specifically, it consists of two parallel triangular bases—one larger than the other—and three rectangular lateral faces that connect the corresponding sides of the two triangular bases.

A triangular hebesphenorotunda is a type of convex polyhedron, which belongs to a specific category of Archimedean solids. To understand it better, it can be described as a truncated version of a triangular prism combined with the properties of other geometric shapes. Here's a breakdown of the name: - **Triangular:** This refers to the shape of the base, specifically that it is a triangle.

A trigonal trapezohedron is a type of polyhedron that has specific characteristics and belongs to the category of trapezohedra. It has 6 faces, each of which is a kite shape. The vertices of a trigonal trapezohedron correspond to the faces of a triangular bipyramid. The trigonal trapezohedron can be thought of as a convex polyhedron that has: - **Faces**: 6 faces, all of which are congruent kites.

A truncated trapezohedron is a type of Archimedean solid derived from the trapezohedron, which itself is a 3D shape with trapezoidal faces. Specifically, a truncated trapezohedron results from truncating (cutting off) the vertices of the original trapezohedron. The geometry of a truncated trapezohedron features a combination of polygons as its faces—specifically, in this case, it will include hexagonal and quadrilateral faces.

"Pi" is an art project created by the artist and designer Martin Vargic. It is known for visualizing the digits of the mathematical constant π (pi) in a unique and creative way. Vargic's work often combines mathematics, art, and data visualization, exploring the intersection of these fields. In the "Pi" project, Vargic typically represents the digits of pi in various artistic formats, including intricate illustrations, infographics, and maps.

A hemi-icosahedron is a geometric shape that can be thought of as half of a regular icosahedron. An icosahedron is a polyhedron with 20 equilateral triangular faces, 30 edges, and 12 vertices. When we talk about a "hemi" version, we typically refer to one of the two symmetrical halves that can be obtained by slicing the icosahedron through its center.