| Augmented dodecahedron | |
|---|---|
 | |
| Type | Johnson J57 – J58 – J59 |
| Faces | 5 triangles 11 pentagons |
| Edges | 35 |
| Vertices | 21 |
| Vertex configuration | 3.5(5) 5(3.5) 1(3) |
| Symmetry group | C5v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the augmented dodecahedron is one of the Johnson solids (J58), consisting of a dodecahedron with a pentagonal pyramid (J2) attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented dodecahedron (J59), a metabiaugmented dodecahedron (J60), or a triaugmented dodecahedron (J61).
A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.
External links
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- Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.