Augmented truncated tetrahedron

In geometry, the augmented truncated tetrahedron is a polyhedron constructed by attaching a triangular cupola onto an truncated tetrahedron.

The augmented truncated tetrahedron is constructed from a truncated tetrahedron by attaching a triangular cupola.

[1] This cupola covers one of the truncated tetrahedron's four hexagonal faces, so that the resulting polyhedron's faces are eight equilateral triangles, three squares, and three regular hexagons.

[2] Since it has the property of convexity and has regular polygonal faces, the augmented truncated tetrahedron is a Johnson solid, denoted as the sixty-fifth Johnson solid

[3] The surface area of an augmented truncated tetrahedron is:[2]

Its volume can be calculated by slicing it off into both truncated tetrahedron and triangular cupola, and adding their volume:[2]

Its dihedral angles can be obtained by adding the angle of a triangular cupola and an augmented truncated tetrahedron in the following:[4]

3D model of an augmented truncated tetrahedron