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).
Metabiaugmented dodecahedronIn 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 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".
