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The truncated dodecahedron is constructed from a regular dodecahedron by cutting all of its vertices off, a process known as truncation. [1] Alternatively, the truncated dodecahedron can be constructed by expansion: pushing away the edges of a regular dodecahedron, forming the pentagonal faces into decagonal faces, as well as the vertices into triangles. [2]
In geometry, the truncated dodecadodecahedron (or stellatruncated dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U 59. It is given a Schläfli symbol t 0,1,2 { 5 ⁄ 3 ,5}. It has 54 faces (30 squares , 12 decagons , and 12 decagrams ), 180 edges, and 120 vertices. [ 1 ]
This polyhedron can be considered a rectified great dodecahedron. It is center of a truncation sequence between a small stellated dodecahedron and great dodecahedron : The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 faces: 12 pentagons from the truncated vertices and 12 overlapping as ...
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 ...
The regular dodecahedron can be interpreted as a truncated trapezohedron. It is the set of polyhedrons that can be constructed by truncating the two axial vertices of a trapezohedron. Here, the regular dodecahedron is constructed by truncating the pentagonal trapezohedron. The regular dodecahedron can be interpreted as the Goldberg polyhedron ...
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 ...
In geometry, the small stellated truncated dodecahedron (or quasitruncated small stellated dodecahedron or small stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U 58. It has 24 faces (12 pentagons and 12 decagrams), 90 edges, and 60 vertices. [1] It is given a Schläfli symbol t{5 ⁄ 3,5}, and Coxeter diagram.
It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms.It additionally shares its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).