View source for Metabiaugmented hexagonal prism

{{Short description|56th Johnson solid}}
{{Infobox polyhedron
|image=metabiaugmented_hexagonal_prism.png
|type=[[Johnson solid|Johnson]]<br>{{math|[[Parabiaugmented hexagonal prism|''J''{{sub|55}}]] – '''''J''{{sub|56}}''' – [[Triaugmented hexagonal prism|''J''{{sub|57}}]]}}
|faces=2x2+4 [[Triangle|triangle]]s <br>2+2 squares <br>2 [[Hexagon|hexagon]]s
|edges=26
|vertices=14
|symmetry={{math|''C''{{sub|2v}}}}
|vertex_config={{math|4(4{{sup|2}}.6)<br>2(3{{sup|4}})<br>2x4(3{{sup|2}}.4.6)}}
|dual=-
|properties=[[Convex polytope|convex]]
|net=Johnson solid 56 net.png
}}

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

{{Johnson solid}}

== See also ==
* [[Hexagonal prism]]

==External links==
* {{MathWorld2 | urlname2=JohnsonSolid | title2=Johnson Solid| urlname=MetabiaugmentedHexagonalPrism  | title= Metabiaugmented hexagonal prism }}

[[Category:Johnson solids]]
{{Johnson solids navigator}}

{{Sourceattribution|Metabiaugmented hexagonal prism}}