Triaugmented triangular prism

In geometry, the triaugmented triangular prism, tetracaidecadeltahedron, or tetrakis triangular prism is one of the Johnson solids (J51). Each of its 14 faces is an equilateral triangle, making it a deltahedron. As the name suggests, it can be constructed by attaching equilateral square pyramids (J1) to each of the three equatorial faces of the triangular prism.

Triaugmented triangular prism
TypeJohnson
J50 - J51 - J52
Faces14 (2+2×6) triangles
Edges21
Vertices9
Vertex configuration3(34)
6(35)
Symmetry groupD3h
Dual polyhedronOrder-4 truncated triangular bipyramid (associahedron K5)
Propertiesconvex, deltahedron
Net

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

Dual polyhedron

The dual of the triaugmented triangular prism is an order-4 truncated triangular bipyramid, also known as an order-5 associahedron. This transparent image shows its three square, and six congruent irregular pentagonal faces. Edges are colored to distinguish the 3 different edge lengths.

  • Weisstein, Eric W. "Triaugmented triangular prism". MathWorld.
  1. Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.
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