Three times the built-up dodecahedron [1] is one of Johnson's polyhedra ( J 61 , according to Zalgaller - M 15 + 3M 3 ).
| Thrice-Extended Dodecahedron | |||
|---|---|---|---|
 ( 3D model ) | |||
| Type of | Johnson's polyhedron | ||
| The properties | convex | ||
| Combinatorics | |||
| Items |
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| Facets | 15 triangles 9 pentagons | ||
| Vertex configuration | 2 + 3 (5 3 ) 3 + 2x6 (3 2 .5 2 ) 3 (3 5 ) | ||
Scan
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| Classification | |||
| Designations | J 61 , M 15 + 3M 3 | ||
| Symmetry group | C 3v | ||
Composed of 24 faces: 15 regular triangles and 9 regular pentagons . Among the pentagonal faces 3 are surrounded by four pentagonal and triangular, the remaining 6 by three pentagonal and two triangular; each triangular face is surrounded by a pentagonal and two triangular.
It has 45 edges of the same length. 15 edges are located between two pentagonal faces, 15 edges are between a pentagonal and triangular, the remaining 15 are between two triangular.
The triple-extended dodecahedron has 23 peaks. Three pentagonal faces converge at 5 vertices; at 15 vertices two pentagonal and two triangular faces converge; five triangular faces converge at 3 vertices.
A three-fold extended dodecahedron can be obtained from four polyhedra - the dodecahedron and three pentagonal pyramids ( J 2 ) - by attaching the base of the pyramids to any three pairwise non-adjacent faces of the dodecahedron.
Metric
If the triple-extended dodecahedron has an edge of length 
Notes
- β Zalgaller V. A. Convex polyhedra with regular edges / Zap. scientific sem. LOMI, 1967. - V. 2. - Page. 22.
Links
- Weisstein, Eric W. Three-fold Dodecahedron on the Wolfram MathWorld .