Triaugmented triangular prism

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Triaugmented triangular prism
Triaugmented triangular prism.png
TypeJohnson
J50 - J51 - J52
Faces14 (2+2×6) triangles
Edges21
Vertices9
Vertex configuration3(34)
6(35)
Symmetry groupD3h
Dual polyhedronassociahedron K5
Propertiesconvex, deltahedron
Net
Johnson solid 51 net.png

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

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[edit]

Dual of triaugmented triangular prism.png

The dual of the triaugmented triangular prism is 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.

External links[edit]

  • 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.