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 c ...

, the triaugmented dodecahedron is one of the

Johnson solid In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johns ...

s (). It can be seen as 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 pentag ...

with three pentagonal pyramids () attached to nonadjacent faces. When pyramids are attached to a dodecahedron in other ways, they may result in an

augmented dodecahedron In geometry, 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 ...

(), a

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

(), a

metabiaugmented dodecahedron In geometry, the metabiaugmented dodecahedron is one of the Johnson solids (). It can be viewed as a dodecahedron with two pentagonal pyramids () attached to two faces that are separated by one face. (The two faces are not opposite, but not adja ...

(), or even a

pentakis dodecahedron In geometry, a pentakis dodecahedron or kisdodecahedron is the polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron; that is, it is the Kleetope of the dodecahedron. It is a Catalan solid, meaning that i ...

if the faces are made to be irregular.

External links

* {{Johnson solids navigator Johnson solids