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]