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  2. Icosahedron - Wikipedia

    en.wikipedia.org/wiki/Icosahedron

    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 ...

  3. Icosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Icosidodecahedron

    Fuller (1975) used these 6 great circles, along with 15 and 10 others in two other polyhedra to define his 31 great circles of the spherical icosahedron. [ 6 ] The long radius (center to vertex) of the icosidodecahedron is in the golden ratio to its edge length; thus its radius is φ if its edge length is 1, and its edge length is ⁠ 1 / φ ...

  4. Polyhedral group - Wikipedia

    en.wikipedia.org/wiki/Polyhedral_group

    The icosahedral group of order 60, rotational symmetry group of the regular dodecahedron and the regular icosahedron. It is isomorphic to A 5. The conjugacy classes of I are: identity; 12 × rotation by ±72°, order 5; 12 × rotation by ±144°, order 5; 20 × rotation by ±120°, order 3; 15 × rotation by 180°, order 2

  5. Icosahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Icosahedral_symmetry

    Icosahedral symmetry fundamental domains A soccer ball, a common example of a spherical truncated icosahedron, has full icosahedral symmetry. Rotations and reflections form the symmetry group of a great icosahedron. In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron.

  6. List of polygons, polyhedra and polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons...

    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)

  7. Kinematics of the cuboctahedron - Wikipedia

    en.wikipedia.org/wiki/Kinematics_of_the_cub...

    [a] What the cuboctahedron transforms into is a regular icosahedron of shorter radius and shorter edge length, a Jessen's icosahedron of still shorter radius and (minimum) edge length, and finally an octahedron of still shorter radius but the same (maximum) edge length as the cuboctahedron (but only after the edges have shortened and lengthened ...

  8. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    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

  9. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    T h – pyritohedral symmetry; the symmetry of a pyritohedron; order 24. O – chiral octahedral symmetry;the rotation group of the cube and octahedron; order 24. O h – full octahedral symmetry; the symmetry group of the cube and octahedron; order 48. I – chiral icosahedral symmetry; the rotation group of the icosahedron and the ...