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1 icosahedron 1 dodecahedron: Faces: 20 triangles 12 pentagons: Edges: 60 Vertices: 32 Symmetry group: icosahedral (I h) In geometry, this polyhedron can be seen as ...
A regular icosahedron can be distorted or marked up as a lower pyritohedral symmetry, [2] [3] and is called a snub octahedron, snub tetratetrahedron, snub tetrahedron, and pseudo-icosahedron. [4] This can be seen as an alternated truncated octahedron .
An icosahedron can be inscribed in a dodecahedron by placing its vertices at the face centers of the dodecahedron, and vice versa. [ 17 ] An icosahedron can be inscribed in an octahedron by placing its 12 vertices on the 12 edges of the octahedron such that they divide each edge into its two golden sections .
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron; Abstract regular polyhedra (Projective polyhedron)
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
arccos (- 1 / 2 ) = 2 π / 3 120° Great rhombic triacontahedron (Dual of great icosidodecahedron) — V(3. 5 / 2 .3. 5 / 2 ) arccos ( √ 5-1 / 4 ) = 2 π / 5 72° Duals of the ditrigonal polyhedra Small triambic icosahedron (Dual of small ditrigonal icosidodecahedron) — V(3. 5 / 2 .3. 5 / ...
Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection ), for a total ...
A regular dodecahedron or pentagonal dodecahedron [notes 1] is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron ...