The truncated tetrahedron is the Archimedean solid with faces 
.
It is also the uniform polyhedron with Maeder
index 2 (Maeder 1997), Wenninger index 6 (Wenninger 1989), Coxeter index 16 (Coxeter
et al. 1954), and Har'El index 7 (Har'El 1993). It has Schläfli
symbol t
and Wythoff symbol 
. It is illustrated above together with a wireframe version
and a net that can be used for its construction.
Some symmetric projections of the truncated tetrahedron are illustrated above.
It is implemented in the Wolfram Language as PolyhedronData["TruncatedTetrahedron"] or UniformPolyhedron["TruncatedTetrahedron"]. Precomputed properties are available as PolyhedronData["TruncatedTetrahedron"].
The skeleton of the truncated tetrahedron is the truncated tetrahedral graph, illustrated above in a number of embeddings.
The dual polyhedron of the truncated tetrahedron is the triakis tetrahedron, both of which
are illustrated above together with their common midsphere.
The inradius 
of the dual, midradius 
of the solid and dual, and circumradius 
of the solid for 
are
 |  |  |
(1)
|
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(2)
|
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(3)
|
The distances from the center of the solid to the centroids of the triangular and hexagonal faces are given by
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(4)
|
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(5)
|
The surface area and volume are
 |  |  |
(6)
|
 |  |  |
(7)
|
The unit truncated tetrahedron has Dehn invariant
 |  |  |
(8)
|
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(9)
|
 |  |  |
(10)
|
(OEIS A377277), where the first expression uses the basis of Conway et al. (1999).
." §3.7.1 in