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Symmetries of a regular hendecagon. Vertices are colored by their symmetry positions. Blue mirror lines are drawn through vertices and edge. Gyration orders are given in the center. The regular hendecagon has Dih 11 symmetry, order 22. Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih 1, and 2 cyclic group symmetries ...
The 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. The regular hexahedron is a cube . Table of polyhedra
Number of vertices V, edges E, Faces F and number of faces by type. Euler characteristic χ = V - E + F The vertex figures are on the left, followed by the Point groups in three dimensions#The seven remaining point groups , either tetrahedral T d , octahedral O h or icosahedral I h .
In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded by alternating faces and edges. The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices.
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices, and 120 edges.
If the truncation is exactly deep enough such that each pair of faces from adjacent vertices shares exactly one point, it is known as a rectification. Expansion involves moving each face away from the center (by the same distance to preserve the symmetry of the Platonic solid) and taking the convex hull.
All vertices are valence-6 except the 12 centered at the original vertices which are valence 5 A geodesic polyhedron is a convex polyhedron made from triangles . They usually have icosahedral symmetry , such that they have 6 triangles at a vertex , except 12 vertices which have 5 triangles.