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The icosahedral pyramid is a four-dimensional convex polytope, bounded by one icosahedron as its base and by 20 triangular pyramid cells which meet at its apex. Since an icosahedron's circumradius is less than its edge length, [1] the tetrahedral pyramids can be made with regular faces. Having all regular cells, it is a Blind polytope.
A regular icosahedron is topologically identical to a cuboctahedron with its 6 square faces bisected on diagonals with pyritohedral symmetry. The icosahedra with pyritohedral symmetry constitute an infinite family of polyhedra which include the cuboctahedron, regular icosahedron, Jessen's icosahedron, and double cover octahedron. Cyclical ...
Square antiprism: Triakis tetrahedron: Elongated triangular bipyramid: Gyrobifastigium: Snub disphenoid: Biaugmented triangular prism: 9 Triangular cupola: Triaugmented triangular prism: Elongated square pyramid: Gyroelongated square pyramid: Tridiminished icosahedron: Octagonal pyramid: Heptagonal bipyramid: 10 Nonagonal pyramid: Octagonal ...
Octagonal prism, Square antiprism, Square cupola, Pentagonal bipyramid, Augmented pentagonal prism Dodecahedron Pentagonal antiprism , Decagonal prism , Pentagonal cupola , Snub disphenoid , Elongated square bipyramid , Metabidiminished icosahedron , Hexagonal bipyramid , Hexagonal trapezohedron , Triakis tetrahedron , Rhombic dodecahedron ...
The icosahedron is the dimensional analogue of the 600-cell, a regular 4-dimensional polytope. The 600-cell has icosahedral cross sections of two sizes, and each of its 120 vertices is an icosahedral pyramid; the icosahedron is the vertex figure of the 600-cell.
Gyroelongated square cupola; Gyroelongated square pyramid; Gyroelongated triangular bicupola; ... Compound of great icosahedron and great stellated dodecahedron;
A related vertex-transitive polytope can be constructed with equal edge lengths removes 120 vertices from the rectified 600-cell, but isn't uniform because it contains square pyramid cells, [1] discovered by George Olshevsky, calling it a swirlprismatodiminished rectified hexacosichoron, with 840 cells (600 square pyramids, 120 pentagonal ...
If the apex of the pyramid is directly above the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges are equal in length, its triangles are all equilateral. It is called an equilateral square pyramid, an example of a Johnson solid.