Augmented dodecahedronIn geometry, the augmented dodecahedron is one of the Johnson solids (J_58), consisting of a dodecahedron with a pentagonal pyramid (J_2) attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented dodecahedron (J_59), a metabiaugmented dodecahedron (J_60), or a triaugmented dodecahedron (J_61).
Parabiaugmented dodecahedronIn 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.
Triaugmented dodecahedronIn 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 solidIn 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".
