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Concept
Metabiaugmented hexagonal prism
Summary
In geometry, the metabiaugmented hexagonal prism is one of the Johnson solids (J_56). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids (J_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.
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Related concepts (3)
Augmented hexagonal prism
In geometry, the augmented hexagonal prism is one of the Johnson solids (J_54). As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid (J_1) to one of its equatorial faces. When two or three such pyramids are attached, the result may be a parabiaugmented hexagonal prism (J_55), a metabiaugmented hexagonal prism (J_56), or a triaugmented hexagonal prism (J_57).
Johnson solid
In 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".
Hexagon
In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. A regular hexagon has Schläfli symbol {6} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).