Concept

Augmented dodecahedron

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Parabiaugmented dodecahedron

In geometry, the parabiaugmented dodecahedron is one of the Johnson solids (J_59). It can be seen as a dodecahedron with two pentagonal pyramids (J_2) attached to opposite faces. When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron (J_58), a metabiaugmented dodecahedron (J_60), a triaugmented dodecahedron (J_61), or even a pentakis dodecahedron if the faces are made to be irregular. The dual of this solid is the Gyroelongated pentagonal bifrustum.

Metabiaugmented dodecahedron

In geometry, the metabiaugmented dodecahedron is one of the Johnson solids (J_60). It can be viewed as a dodecahedron with two pentagonal pyramids (J_2) attached to two faces that are separated by one face. (The two faces are not opposite, but not adjacent either.) When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron (J_58), a parabiaugmented dodecahedron (J_59), a triaugmented dodecahedron (J_61), or even a pentakis dodecahedron if the faces are made to be irregular.

Triaugmented dodecahedron

In geometry, the triaugmented dodecahedron is one of the Johnson solids (J_61). It can be seen as a dodecahedron with three pentagonal pyramids (J_2) attached to nonadjacent faces. When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron (J_58), a parabiaugmented dodecahedron (J_59), a metabiaugmented dodecahedron (J_60), or even a pentakis dodecahedron if the faces are made to be irregular.

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 Johnson solid is the square-based pyramid with equilateral sides (J_1); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform (i.e., not Platonic solid, Archimedean solid, uniform prism, or uniform antiprism) before they refer to it as a "Johnson solid".