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The pentagonal icositetrahedron can be constructed from a snub cube without taking the dual. Square pyramids are added to the six square faces of the snub cube, and triangular pyramids are added to the eight triangular faces that do not share an edge with a square.
A regular tetrahedron, an example of a solid with full tetrahedral symmetry. A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
Drawing and crystal model of variant with tetrahedral symmetry called hexakis tetrahedron [1] In geometry , a tetrakis hexahedron (also known as a tetrahexahedron , hextetrahedron , tetrakis cube , and kiscube [ 2 ] ) is a Catalan solid .
In geometry, a disdyakis triacontahedron, hexakis icosahedron, decakis dodecahedron, kisrhombic triacontahedron [1] or d120 is a Catalan solid with 120 faces and the dual to the Archimedean truncated icosidodecahedron.
Reuleaux tetrahedron. The Reuleaux tetrahedron is the intersection of four balls of radius s centered at the vertices of a regular tetrahedron with side length s. [1] The spherical surface of the ball centered on each vertex passes through the other three vertices, which also form vertices of the Reuleaux tetrahedron.
In Magnus Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+} b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, and q-valence vertices.
Polytetrahedron is a term used for three distinct types of objects, all based on the tetrahedron: A uniform convex 4-polytope made up of 600 tetrahedral cells. It is more commonly known as a 600-cell or hexacosichoron. Other derivative 4-polytope are identified as polytetrahedra, where a qualifying prefix such as rectified or truncated is used.
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