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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 ...
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 ...
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 ...
A regular dodecahedron or pentagonal dodecahedron [notes 1] is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids , described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler .
There are no nonconvex Euclidean regular tessellations in any number of dimensions. Polytope elements ... Truncated rhombic dodecahedron; Truncated trapezohedron;
2 Dimensions. 3 Geometric relations. ... with icosidodecahedral rhombus being his name for a rhombic triacontahedron. ... the small stellated truncated dodecahedron, ...
The rhombic dodecahedron, with two types of alternating vertices, 8 with three rhombic faces, and 6 with four rhombic faces. ... In higher dimensions, Coxeter defined ...
Their duals, the rhombic dodecahedron and rhombic triacontahedron, ... In three dimensions, these coincide with the tetrahedron as {3,3}, the cube as {4,3}, and the ...