geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, the augmented dodecahedron is one of the Johnson solids (), consisting of a

dodecahedron In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...

with a

pentagonal pyramid In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the apex). Like any pyramid, it is self- dual. The ''regular'' pentagonal pyramid has a base that is a regu ...

() attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented dodecahedron (), a metabiaugmented dodecahedron (), or a

triaugmented dodecahedron In geometry, the triaugmented dodecahedron is one of the Johnson solids (). It can be seen as a dodecahedron with three pentagonal pyramids () attached to nonadjacent faces. When pyramids are attached to a dodecahedron in other ways, they may re ...

().

External links

* Johnson solids {{Polyhedron-stub