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The regular tetrahedron is self-dual, meaning its dual is another regular tetrahedron. The compound figure comprising two such dual tetrahedra form a stellated octahedron or stella octangula . Its interior is an octahedron , and correspondingly, a regular octahedron is the result of cutting off, from a regular tetrahedron, four regular ...
The 5-cell is the 4-dimensional simplex, the simplest possible 4-polytope.In other words, the 5-cell is a polychoron analogous to a tetrahedron in high dimension. [4] It is formed by any five points which are not all in the same hyperplane (as a tetrahedron is formed by any four points which are not all in the same plane, and a triangle is formed by any three points which are not all in the ...
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.
A net of a regular dodecahedron The eleven nets of a cube. In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.
The research of examples of this particular nets dates back to the end of the 20th century, despite that, not many examples have been found. Two classes, however, have been deeply explored, regular polyhedra and cuboids. The search of common nets is usually made by either extensive search or the overlapping of nets that tile the plane.
The next most regular convex polyhedra after the Platonic solids are the cuboctahedron, which is a rectification of the cube and the octahedron, and the icosidodecahedron, which is a rectification of the dodecahedron and the icosahedron (the rectification of the self-dual tetrahedron is a regular octahedron).
Net In geometry , the Rhombicosidodecahedron is an Archimedean solid , one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces . It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices , and 120 edges .
Net. In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called a C 120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron [1] and hecatonicosahedroid.