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The rhombic dodecahedron forms the maximal cross-section of a 24-cell, and also forms the hull of its vertex-first parallel projection into three dimensions. The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24 ...
Rhombic hexahedron (Dual of tetratetrahedron) — V(3.3.3.3) arccos (0) = π / 2 90° Rhombic dodecahedron (Dual of cuboctahedron) — V(3.4.3.4) arccos (- 1 / 2 ) = 2 π / 3 120° Rhombic triacontahedron (Dual of icosidodecahedron) — V(3.5.3.5) arccos (- √ 5 +1 / 4 ) = 4 π / 5 144° Medial rhombic ...
The concave equilateral dodecahedron, called an endo-dodecahedron. [clarification needed] A cube can be divided into a pyritohedron by bisecting all the edges, and faces in alternate directions. A regular dodecahedron is an intermediate case with equal edge lengths. A rhombic dodecahedron is a degenerate case with the 6 crossedges reduced to ...
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 ...
There are no nonconvex Euclidean regular tessellations in any number of dimensions. Polytope elements ... Truncated rhombic dodecahedron; Truncated trapezohedron;
In geometry, the rhombicuboctahedron is an Archimedean solid with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by Johannes Kepler in his 1618 Harmonices Mundi, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.
rhombic dodecahedron: 12 rhombi: 24 14 120° O h: triakis octahedron: 24 isosceles triangles 36 14 147.350° O h: tetrakis hexahedron: 24 isosceles triangles 36 14 143.130° O h: deltoidal icositetrahedron: 24 kites: 48 26 138.118° O h: disdyakis dodecahedron: 48 scalene triangles: 72 26 155.082° O h: pentagonal icositetrahedron: 24 pentagons ...
Each vertex with the obtuse rhombic face angles is shared by 4 cells; each vertex with the acute rhombic face angles is shared by 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron , which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal ...