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 
, the resulting polyhedron has surface
area and volume given by
 |  |  |
(1)
|
 |  |  |
(2)
|
The convex hull of this polyhedron is the triakis tetrahedron.
