Augmented Tetrahedron

An augmented tetrahedron is an augmented polyhedron obtained by augmenting the four faces of a tetrahedron with four tetrahedra, leading to a concave polyhedron with 8 vertices, 18 edges, and 12 faces. It is therefore a (non-regular, concave) dodecahedron.


When the base tetrahedron is a regular tetrahedron, the resulting equilateral polyhedron is a concave deltahedron, illustrated above and implemented in the Wolfram Language as PolyhedronData["EquilateralAugmentedTetrahedron"]. For a base tetrahedron with edge lengths a, the resulting polyhedron has surface area and volume given by


The convex hull of this polyhedron is the triakis tetrahedron.

See also

Augmentation, Augmented Polyhedron, Deltahedron, Regular Tetrahedron, Tetrahedron, Tritetrahedron

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Cite this as:

Weisstein, Eric W. "Augmented Tetrahedron." From MathWorld--A Wolfram Web Resource.

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