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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 .
Regular icosahedron itself is the zeroth stellation of an icosahedron, and the subsequent stellation is obtained by radiating spikes from the faces of a regular icosahedron. The final stellation includes all of the cells in the icosahedron's stellation diagram, meaning every three intersecting face planes of the icosahedral core intersect ...
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.
A dodecahedron and its dual icosahedron The intersection of both solids is the icosidodecahedron , and their convex hull is the rhombic triacontahedron . Seen from 2-fold, 3-fold and 5-fold symmetry axes
Name picture Faces Edges Vertices Vertex configuration icosidodecahedron (quasi-regular: vertex- and edge-uniform) (32: 20 triangles 12 pentagons: 60: 30 3,5,3,5
3D model of a great icosahedron. In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3, 5 ⁄ 2} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence.
The icosahedron, as a uniform snub tetrahedron, is similar to these snub-pair compounds: compound of two snub cubes and compound of two snub dodecahedra. Together with its convex hull, it represents the icosahedron-first projection of the nonuniform snub tetrahedral antiprism.
A rhombic icosahedron. The rhombic icosahedron is a polyhedron shaped like an oblate sphere.Its 20 faces are congruent golden rhombi; [1] 3, 4, or 5 faces meet at each vertex. It has 5 faces (green on top figure) meeting at each of its 2 poles; these 2 vertices lie on its axis of 5-fold symmetry, which is perpendicular to 5 axes of 2-fold symmetry through the midpoints of opposite equatorial ...