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The regular dodecahedron's metric properties and construction are associated with the golden ratio. The regular dodecahedron can be found in many popular cultures: Roman dodecahedron, the children's story, toys, and painting arts. It can also be found in nature and supramolecules, as well as the shape of the universe.
In geometry, a dodecahedron (from Ancient Greek δωδεκάεδρον (dōdekáedron); from δώδεκα (dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron [1] is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices, and 120 edges.
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
The dodecahedron is a regular polyhedron with Schläfli symbol {5,3}, having 3 pentagons around each vertex.. In geometry, the Schläfli symbol is a notation of the form {,,,...} that defines regular polytopes and tessellations.
The regular dodecagon is the Petrie polygon for many higher-dimensional polytopes, seen as orthogonal projections in Coxeter planes. Examples in 4 dimensions are the 24-cell, snub 24-cell, 6-6 duoprism, 6-6 duopyramid. In 6 dimensions 6-cube, 6-orthoplex, 2 21, 1 22. It is also the Petrie polygon for the grand 120-cell and great stellated 120-cell.
Uniform polyhedra are vertex-transitive and every face is a regular polygon. They may be subdivided into the regular, quasi-regular, or semi-regular, and may be convex or starry. The duals of the uniform polyhedra have irregular faces but are face-transitive, and every vertex figure is a regular polygon. A uniform polyhedron has the same ...
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 ]