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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 ...
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. However, the regular dodecahedron ...
A Roman dodecahedron or Gallo-Roman dodecahedron [1] [2] is a small hollow object made of copper alloy which has been cast into a regular dodecahedral shape with twelve flat pentagonal faces. Each face has a circular hole of varying diameter in the middle, the holes connecting to the hollow center, and each corner has a protruding knob. [ 1 ]
The release describes the dodecahedron as “one of the largest examples” discovered. However, experts still aren’t sure exactly what the Romans used the dodecahedron for.
The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors. The balls are "expanded" rhombicosidodecahedra, with the squares replaced ...
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb.
The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is internal to its dual, the small stellated dodecahedron. This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} " decagram "); this series continues into the fourth ...
The dyakis dodecahedron can be constructed by enlarging 24 of the 48 faces of the disdyakis dodecahedron and is inscribed in the dyakis dodecahedron, [2] [page needed] thus it exists as a hemihedral form of it with indices {hkl}. [3] It can be constructed into two non-regular pentagonal dodecahedra, the pyritohedron and the tetartoid.