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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 ...
An isodynamic tetrahedron is one in which the cevians that join the vertices to the incenters of the opposite faces are concurrent, and an isogonic tetrahedron has concurrent cevians that join the vertices to the points of contact of the opposite faces with the inscribed sphere of the tetrahedron.
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.
English: This shows the materials science tetrahedron, which illustrates how a material's properties, processing, performance, and structure are interrelated. It is based on its having prior use in my engineering studies as a teaching device and symbol of the discipline, using this file as a reference.
The tetrahedron is self-dual (i.e. its dual is another tetrahedron). The cube and the octahedron form a dual pair. The dodecahedron and the icosahedron form a dual pair. If a polyhedron has Schläfli symbol {p, q}, then its dual has the symbol {q, p}. Indeed, every combinatorial property of one Platonic solid can be interpreted as another ...
The illustration here shows the vertex figure (red) of the cuboctahedron being used to derive the corresponding face (blue) of the rhombic dodecahedron.. For a uniform polyhedron, each face of the dual polyhedron may be derived from the original polyhedron's corresponding vertex figure by using the Dorman Luke construction. [2]
Tetrahedron: 6: Trigonal prism: 8: Cube: 10: Pentagonal prism: 12: D 2d pseudo-octahedron (dual of snub disphenoid) 14: Dual of triaugmented triangular prism (K 5 associahedron) 16: Square truncated trapezohedron: 18: Dual of edge-contracted icosahedron 20: Dodecahedron
By definition, this isotopic property is common to the duals of the uniform polytopes. An isotopic 2-dimensional figure is isotoxal, i.e. edge-transitive. An isotopic 3-dimensional figure is isohedral, i.e. face-transitive. An isotopic 4-dimensional figure is isochoric, i.e. cell-transitive.