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The Great icosihemidodecacron, often referred to as a "great icosihemidodecahedron," is a complex geometric shape. It belongs to the category of convex polyhedra and is an Archimedean dual of the rhombicosidodecahedron. It is defined as a polyhedron with 62 faces consisting of 20 triangles, 30 squares, and 12 regular pentagons.

The great icosihemidodecahedron is a type of Archimedean solid, which is a convex polyhedron characterized by having regular polygons as its faces and exhibiting a high degree of symmetry. Specifically, it is one of the non-convex uniform polyhedra.

The great inverted snub icosidodecahedron is a geometrical figure that falls into the category of Archimedean solids. It is an interesting and complex polyhedron that has a high degree of symmetry and an intricate structure. ### Characteristics: - **Faces:** The great inverted snub icosidodecahedron has 62 faces, which consist of 20 regular hexagons and 42 equilateral triangles. - **Vertices:** It has 120 vertices.

The Great Pentagrammic Hexecontahedron is a complex geometric shape classified as a non-convex polyhedron. It is part of a larger family of shapes known as polyhedra. Specifically, it is one of the Archimedean duals, sometimes referred to as the "dual polyhedra" of the great icosahedron.

The great pentakis dodecahedron is a type of convex polyhedron and belongs to the family of Archimedean solids. It can be thought of as a variation of the dodecahedron, which has 12 regular pentagonal faces. The great pentakis dodecahedron is characterized by having 60 triangular faces.

The great retrosnub icosidodecahedron is a non-convex uniform polyhedron and is one of the Archimedean solids. It is characterized by its complex structure, which consists of a combination of regular polygons. Specifically, the great retrosnub icosidodecahedron has the following properties: - **Faces**: It consists of 62 faces, which include 20 regular triangles, 12 regular pentagons, and 30 squares.

The great rhombic triacontahedron is a type of convex Archimedean solid, which is a class of polyhedra characterized by having regular polygons as their faces, with the same arrangement of faces around each vertex.

The great rhombidodecacoron is a convex uniform polychoron (a four-dimensional shape) in the context of higher-dimensional geometry. It is categorized under the family of Archimedean solids, specifically as a uniform spatial structure extending into four dimensions. This shape is distinguished by its vertices, edges, and faces, where it consists of 120 rhombic faces and 60 dodecahedral cells.

The great rhombidodecahedron is one of the Archimedean solids, a category of convex polyhedra characterized by their vertex-transitivity and consistent face types. This particular solid has a unique geometric structure that comprises 62 faces, which includes 12 regular pentagons and 50 regular hexagons. In terms of its vertices, the great rhombidodecahedron has 120 vertices and 180 edges.

The great rhombihexahedron is a type of convex polyhedron and is one of the Archimedean solids. It is characterized by having 12 faces, all of which are rhombuses, and a total of 24 edges and 14 vertices. The great rhombihexahedron has a unique and symmetrical geometric structure. Its vertices can be described using a specific set of coordinates in three-dimensional space.

The great snub dodecicosidodecahedron is a type of Archimedean solid, which is a highly symmetrical, convex polyhedron with regular faces of more than one type. Specifically, the great snub dodecicosidodecahedron features: - **Faces**: It has a total of 92 faces, comprised of 12 regular pentagons, 20 regular hexagons, and 60 equilateral triangles.

The great stellapentakis dodecahedron is a convex polyhedron in the category of stellated polyhedra. It is one of the many tessellated shapes in the field of geometry and is characterized by a specific arrangement of its faces, vertices, and edges. To break it down: 1. **Dodecahedron**: This is a polyhedron with 12 flat faces, each of which is a regular pentagon.

The great stellated truncated dodecahedron is a type of Archimedean solid, a category of geometric shapes characterized by their regular vertex arrangement, composed of two or more types of regular polygons. Specifically, the great stellated truncated dodecahedron consists of 12 regular pentagram faces (star polygons) and 20 regular hexagonal faces.

The Great Triakis Icosahedron is a type of convex polyhedron and one of the Archimedean solids. It can be understood as an augmentation of the regular icosahedron, where each triangular face of the icosahedron is subdivided into smaller triangles. Specifically, each face of the icosahedron is divided into three smaller triangles, with an added pyramid atop each of these newly created triangular faces.

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.

The Great Truncated Cuboctahedron is a unique type of Archimedean solid, which is a class of polyhedra characterized by having regular polygons as their faces and being vertex-transitive. Specifically, the Great Truncated Cuboctahedron is derived from the cuboctahedron by truncating its vertices and further truncating the resulting edges.

The great truncated icosidodecahedron is a convex Archimedean solid. It is one of the many uniform polyhedra that have regular polygonal faces and exhibit vertex transitivity. Here are some key characteristics of the great truncated icosidodecahedron: 1. **Faces**: It has a total of 62 faces, which include 20 regular hexagons, 12 regular decagons, and 30 squares.

The gyrate bidiminished rhombicosidodecahedron is a complex geometric shape classified as an Archimedean solid. To break down its name: 1. **Gyrate**: This term usually indicates that the shape is a twisted or rotated version of a similar standard form, which introduces a certain symmetry or alteration to the standard polyhedron.

The term "gyrate rhombicosidodecahedron" refers to a specific type of convex polyhedron that is a variation of the rhombicosidodecahedron. A rhombicosidodecahedron is one of the Archimedean solids, characterized by its 62 faces, which include 20 equilateral triangles, 30 squares, and 12 regular pentagons. It has 60 edges and 20 vertices.

A gyroelongated bicupola is a type of polyhedron that is part of the family of Archimedean solids. It is formed by joining two identical cupolae (which are polyhedral structures with a polygonal base and a series of triangular faces leading to a point) with a cylindrical section that is elongated around the axis of symmetry.