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The rectified polyhedron turns out to be expressible as the intersection of the original platonic solid with an appropriately scaled concentric version of its dual. For this reason, its name is a combination of the names of the original and the dual:
The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. ... Rectified cubic honeycomb;
Any regular polyhedron or tiling Rectified (r) r{p,q} t 1 {p,q} The edges are fully truncated into single points. The polyhedron now has the combined faces of the parent and dual. Polyhedra are named by the number of sides of the two regular forms: {p,q} and {q,p}, like cuboctahedron for r{4,3} between a cube and octahedron. Birectified (2r ...
The triangle and squares of the rhombicuboctahedron can be independently rectified or truncated, creating four permutations of polyhedra. The partially truncated forms can be seen as edge contractions of the truncated form. The truncated rhombicuboctahedron can be seen in sequence of rectification and truncation operations from the cuboctahedron.
The expanded cuboctahedron is a polyhedron constructed by expansion of the cuboctahedron. It has 50 faces: 8 triangles, 30 squares, and 12 rhombs. The 48 vertices exist at two sets of 24, with a slightly different distance from its center. It can also be constructed as a rectified rhombicuboctahedron.
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.
Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) ... Quasiregular polyhedra (Rectified regular) Tetratetrahedron: r{3,3} (3.3.3.3)
In geometry, the rectified truncated tetrahedron is a polyhedron, constructed as a rectified, truncated tetrahedron. It has 20 faces: 4 equilateral triangles , 12 isosceles triangles , and 4 regular hexagons .