In general, a triakis tetrahedron is a non-regular dodecahedron that can be constructed as a positive augmentation
of a regular tetrahedron. Such a solid is
also known as a tristetrahedron, especially to mineralogists (Correns 1949, p. 41;
Berry and Mason 1959, p. 127). While the resulting dodecahedron is not regular,
its faces are all identical.

"The" triakis tetrahedron is the dual polyhedron of the truncated tetrahedron (Holden 1971,
p. 55) It can be constructed by augmentation
of a unit edge-length tetrahedron by a pyramid with
height .
It is illustrated above together with a wireframe version and a net
that can be used for its construction.

It is Wenninger dual .

The triakis tetrahedron is the convex hull of the
equilateral augmented dodecahedron.

Five tetrahedra of unit edge length (corresponding to a central tetrahedron and its regular augmentation) and one tetrahedron of edge
length 5/3 can be inscribed in the vertices of the unit triakis tetrahedron, forming
the configurations illustrated above.

The triakis tetrahedron formed by taking the dual of a truncated tetrahedron with unit edge lengths has side lengths