Wikipedia Bot @wikibot 0

The term "metabiaugmented truncated dodecahedron" likely refers to a specific type of polyhedron that is derived from a truncated dodecahedron through augmentation and a technique related to meta-geometry or a particular geometric construction. To understand it better, let's break down the components: 1. **Truncated Dodecahedron**: This is a Archimedean solid formed by truncating (or cutting off) the vertices of a regular dodecahedron.

The term "metabidiminished icosahedron" appears to refer to a geometric shape derived from the icosahedron, one of the five Platonic solids. The icosahedron is a three-dimensional shape with 20 triangular faces, 12 vertices, and 30 edges. The prefix "meta-" and the term "diminished" often indicate some transformation of the original shape.

The term "metabidiminished rhombicosidodecahedron" refers to a specific type of Archimedean solid. Archimedean solids are convex polyhedra with identical vertices and faces made up of two or more types of regular polygons.

The term "metabigyrate rhombicosidodecahedron" describes a specific type of geometric solid that has properties related to both symmetrical transformations and a particular class of polyhedra. 1. **Rhombicosidodecahedron**: This is an Archimedean solid with 62 faces (20 triangular, 30 square, and 12 pentagonal), 120 edges, and 60 vertices.

A monostatic polytope is a specific type of geometric structure in the field of polytopes and geometry. It is defined as a polytope that has one static (or "monostatic") support configuration when it is in equilibrium under the influence of gravity. In practical terms, a monostatic polytope will come to rest on a flat surface in only one stable orientation.

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.

The nonconvex great rhombicuboctahedron is a type of polyhedron that belongs to the category of Archimedean solids. It is classified as a nonconvex solid due to its shape, which includes inwardly drawn faces. ### Characteristics: 1. **Base Shape**: The nonconvex great rhombicuboctahedron has a structure that combines elements of various shapes, specifically squares and triangles.

An octagonal antiprism is a type of polyhedron that belongs to the category of antiprisms. Specifically, it is characterized by two parallel octagonal bases that are connected by a band of triangles. Here are some key features of the octagonal antiprism: 1. **Faces**: It has a total of 18 faces, consisting of 2 octagonal bases and 16 triangular lateral 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.

An octagonal prism is a three-dimensional geometric shape that consists of two parallel octagonal bases and rectangular lateral faces. The structure is characterized by the following properties: 1. **Bases**: It has two octagonal bases that are congruent and parallel to each other. 2. **Faces**: It has a total of 10 faces—2 octagonal faces (the bases) and 8 rectangular faces that connect the corresponding sides of the octagonal bases.

An octagrammic antiprism is a type of polyhedron that belongs to the category of antiprisms. Specifically, it is characterized by its regular octagram faces and a two-layer structure, similar to that of a traditional antiprism. ### Key Characteristics: 1. **Faces**: The octagrammic antiprism has two parallel octagram faces (eight-pointed stars) and additional rectangular faces connecting each edge of one octagram to the corresponding edge of the other.

The octagrammic crossed-antiprism is a type of geometric structure that can be categorized within the broader family of polyhedra. Specifically, it is a semi-regular polyhedron, meaning it has symmetrical properties but does not consist of only one type of regular polygon.

An octagrammic prism is a type of geometric solid that consists of two parallel octagrammic bases (octagrams are eight-pointed stars) connected by rectangular (or square) lateral faces. In three-dimensional space, it is classified as a prism because it has two congruent polygonal bases and parallelogram side faces. ### Key Characteristics: 1. **Base Shape**: The bases are in the shape of an octagram, which is a star polygon with eight points.

An octahemioctahedron is a type of convex polyhedron that is classified as a member of the Archimedean solids. Specifically, it features two types of faces: regular hexagons and equilateral triangles. It has a total of 14 faces, which consists of 8 triangular faces and 6 hexagonal faces.

The order-5 truncated pentagonal hexecontahedron is a type of convex polyhedron that is classified as an Archimedean solid. It is derived from the pentagonal hexecontahedron by truncating its vertices. Specifically, the pentagonal hexecontahedron is a polyhedron composed of 60 triangular faces and 12 pentagonal faces.

The term "parabiaugmented dodecahedron" refers to a specific geometric figure that is a type of convex polyhedron. It is derived from the dodecahedron, which is a Platonic solid with 12 regular pentagonal faces. The "parabiaugmented" part of the name indicates that the dodecahedron has been modified or augmented in a specific way.

A parabiaugmented hexagonal prism is a type of polyhedron that is derived from a hexagonal prism by adding two additional faces based on parabolic shapes. The base of the prism consists of two hexagonal faces connected by six rectangular faces, similar to a standard hexagonal prism. The term "parabiaugmented" indicates that the top and bottom hexagonal faces are augmented or extended with parabolic shapes.

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.

The term "parabidiminished rhombicosidodecahedron" refers to a specific type of geometric figure that belongs to the family of Archimedean solids. The rhombicosidodecahedron is one of the Archimedean solids, known for having 62 faces (20 regular triangles, 30 squares, and 12 regular pentagons), 120 edges, and 60 vertices.

The term "parabigyrate rhombicosidodecahedron" refers to a specific type of geometric figure within the category of Archimedean solids. The rhombicosidodecahedron itself is one of the Archimedean solids, characterized by having 62 faces: 20 regular triangles, 30 squares, and 12 regular pentagons. It has 60 edges and 30 vertices.