Search results
Results from the WOW.Com Content Network
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 ...
The pyritohedral symmetry is an index 5 subgroup of icosahedral symmetry, with 3 orthogonal green reflection lines and 8 red order-3 gyration points. There are 5 different orientations of pyritohedral symmetry.
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
The pyritohedral group T h with fundamental domain The seams of a volleyball have pyritohedral symmetry. T h, 3*2, [4,3 +] or m 3, of order 24 – pyritohedral symmetry. [1] This group has the same rotation axes as T, with mirror planes through two of the orthogonal directions. The 3-fold axes are now S 6 (3) axes
An object of C 3v symmetry under one of the 3-fold axes gives rise under the action of T d to an orbit consisting of four such objects, and T d corresponds to the set of permutations of these four objects. T d is a normal subgroup of O h. See also the isometries of the regular tetrahedron. T h, (3*2) [3 +,4] 2/m 3, m 3 order 24: pyritohedral ...
The cuboctahedron's kinematics is noteworthy in that its vertices can be repositioned to the vertex positions of the regular icosahedron, the Jessen's icosahedron, and the regular octahedron, in accordance with the pyritohedral symmetry of the icosahedron. [1] [2]
Small triambic icosahedron Medial triambic icosahedron Great triambic icosahedron Compound of five octahedra Compound of five tetrahedra Compound of ten tetrahedra Great icosahedron Excavated dodecahedron Final stellation; The stellation process on the icosahedron creates a number of related polyhedra and compounds with icosahedral symmetry
The full symmetry group of the icosahedron (including reflections) is known as the full icosahedral symmetry. [14] It is isomorphic to the product of the rotational symmetry group and the cyclic group of size two, generated by the reflection through the center of the regular icosahedron. [15]