In geometry, the triangular hebesphenorotunda is a Johnson solid with 13 equilateral triangles, 3 squares, 3 regular pentagons, and 1 regular hexagon, meaning the total of its faces is 20.

The triangular hebesphenorotunda is named by Johnson (1966), with the prefix hebespheno- referring to a blunt wedge-like complex formed by three adjacent lunes—a figure where two equilateral triangles are attached at the opposite sides of a square.

The suffix (triangular) -rotunda refers to the complex of three equilateral triangles and three regular pentagons surrounding another equilateral triangle, which bears a structural resemblance to the pentagonal rotunda.

[1] Therefore, the triangular hebesphenorotunda has 20 faces: 13 equilateral triangles, 3 squares, 3 regular pentagons, and 1 regular hexagon.

[2] The faces are all regular polygons, categorizing the triangular hebesphenorotunda as a Johnson solid, enumerated the last one

[3] It is an elementary polyhedron, meaning that it cannot be separated by a plane into two small regular-faced polyhedra.

[4] The surface area of a triangular hebesphenorotunda of edge length

The triangular hebesphenorotunda with edge length

can be constructed by the union of the orbits of the Cartesian coordinates:

τ

2 τ

τ ,

τ

τ , −

τ

τ

under the action of the group generated by rotation by 120° around the z-axis and the reflection about the yz-plane.

denotes the golden ratio.