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Triaugmented Triangular Prism


J51Deltahedron14Net

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular prism.It is a convex deltahedra composed of 14 equilateral triangles.

It is implemented in the Wolfram Language as PolyhedronData["TriaugmentedTriangularPrism"].

The skeleton of the triaugmented triangular prism is the Fritsch graph.

The polyhedron vertices are (+/-1/2,+/-1/2,0), (0,0,sqrt(2)/2), (0,+/-1/2,-sqrt(3)/2), (+/-(1+sqrt(6))/4,0,-(sqrt(2)+sqrt(3))/4), where the x and z coordinates of the last are found by solving

x^2+(1/2)^2+(z+sqrt(3)/2)^2=1^2
(1)
(x-1/2)^2+(1/2)^2+z^2=1^2.
(2)

For a triaugmented triangular prism with unit side length, the surface area and volume are

S=7/2sqrt(3)
(3)
V=1/4(2sqrt(2)+sqrt(3)).
(4)

See also

Augmentation, Deltahedron, Fritsch Graph, Johnson Solid, Triangular Prism

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Triaugmented Triangular Prism." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriaugmentedTriangularPrism.html

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