metabiaugmented hexagonal prism

{{Short description|56th Johnson solid}}

{{Infobox polyhedron

|image=metabiaugmented_hexagonal_prism.png

|type=Johnson
{{math|parabiaugmented hexagonal prism – J{{sub|56}} – triaugmented hexagonal prism}}

|faces=2x2+4 triangles
2+2 squares
2 hexagons

|edges=26

|vertices=14

|symmetry={{math|C{{sub|2v}}}}

|vertex_config={{math|4(4{{sup|2}}.6)
2(3{{sup|4}})
2x4(3{{sup|2}}.4.6)}}

|dual=-

|properties=convex

|net=Johnson solid 56 net.png

}}

In geometry, the metabiaugmented hexagonal prism is one of the Johnson solids ({{math|J{{sub|56}}}}). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids ({{math|J{{sub|1}}}}) to two of its nonadjacent, nonparallel equatorial faces. Attaching the pyramids to opposite equatorial faces yields a parabiaugmented hexagonal prism. (The solid obtained by attaching pyramids to adjacent equatorial faces is not convex, and thus not a Johnson solid.)

{{Johnson solid}}