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A truncated cube with its octagonal faces pyritohedrally dissected with a central vertex into triangles and pentagons, creating a topological icosidodecahedron. Cartesian coordinates for the vertices of a truncated hexahedron centered at the origin with edge length 2 1 / δ S are all the permutations of (± 1 / δ S , ±1, ±1 ...
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square.
Faces by sides: 30{4}+20{6} Coxeter diagram ... It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) ...
Examples colored by the number of sides on each face. Yellow triangles, red squares, and green pentagons. A tesseract projected into 3-space as a Schlegel diagram. There are 8 cubic cells visible: the outer cell into which the others are projected, one below each of the six exterior faces, and one in the center.
The convex forms are listed in order of degree of vertex configurations from 3 faces/vertex and up, and in increasing sides per face. This ordering allows topological similarities to be shown. This ordering allows topological similarities to be shown.
Geodesic subdivisions can also be done from an augmented dodecahedron, dividing pentagons into triangles with a center point, and subdividing from that Chiral polyhedra with higher order polygonal faces can be augmented with central points and new triangle faces. Those triangles can then be further subdivided into smaller triangles for new ...
The truncated octahedron has 14 faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a 6 - zonohedron . It is also the Goldberg polyhedron G IV (1,1), containing square and hexagonal faces.