Augmented dodecahedron
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| Augmented dodecahedron | |
|---|---|
 | |
| Type | Johnson J57 – J58 – J59 |
| Faces | 5 triangles 11 pentagons |
| Edges | 35 |
| Vertices | 21 |
| Vertex configuration | 3.5(53) 5(32.52) 1(35) |
| Symmetry group | C5v |
| Properties | convex |
| Net | |
 | |
In geometry, the augmented dodecahedron is a Johnson solid combining a regular dodecahedron and a pentagonal pyramid.
An augmented dodecahedron is constructed from a regular dodecahedron, a twelve-sided polyhedron with regular pentagons, by attaching a regular-faced pentagonal pyramid to one of the regular dodecahedron's faces; the regular polygons mean that all of its internal angles and edges are equal. The resulting polyhedron covers one pentagon from a dodecahedron with five equilateral triangles from the pyramid. Ergo, the augmented dodecahedron has eleven pentagonal faces and five equilateral triangular faces, totaling sixteen faces.[1] The augmented is Johnson solid, a convex polyhedron with regular faces, enumerated as the fifty-eighth .[2]
