In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the augmented triangular prism is one of the Johnson solid

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...

s (J₄₉). As the name suggests, it can be constructed by augmenting a triangular prism

Prism (geometry)

In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...

 by attaching a square pyramid

Square pyramid

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.- Johnson solid :...

 (J₁) to one of its equatorial faces. The resulting solid bears a superficial resemblance to the gyrobifastigium

Gyrobifastigium

In geometry, the gyrobifastigium is the 26th Johnson solid . It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a half-turn to one prism....

 (J₂₆), the difference being that the latter is constructed by attaching a second triangular prism, rather than a square pyramid.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

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