parabiaugmented hexagonal prism

{{Short description|55th Johnson solid}}

{{Infobox polyhedron

|image=parabiaugmented_hexagonal_prism.png

|type=Johnson
{{math|augmented hexagonal prism – J{{sub|55}} – metabiaugmented hexagonal prism}}

|faces=2x4 triangles
4 squares
2 hexagons

|edges=26

|vertices=14

|symmetry={{math|D{{sub|2h}}}}

|vertex_config={{math|4(4{{sup|2}}.6)
2(3{{sup|4}})
8(3{{sup|2}}.4.6)}}

|dual=parabilaterotruncated hexagonal bipyramid

|properties=convex

|net=Johnson solid 55 net.png

}}

In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids ({{math|J{{sub|55}}}}). 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, parallel (opposite) equatorial faces. Attaching the pyramids to nonadjacent, nonparallel equatorial faces yields a metabiaugmented hexagonal prism ({{math|J{{sub|56}}}}). (The solid obtained by attaching pyramids to adjacent equatorial faces is not convex, and thus not a Johnson solid.)

{{Johnson solid}}