Editing Triangular hebesphenorotunda (section)

== Properties ==
The triangular hebesphenorotunda is named by {{harvtxt|Johnson|1966}}, with the prefix ''hebespheno-'' referring to a blunt wedge-like complex formed by three adjacent ''lunes''&mdash;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]].{{r|johnson}} Therefore, the triangular hebesphenorotunda has 20 faces: 13 [[equilateral triangle]]s, 3 [[Square (geometry)|square]]s, 3 [[regular pentagon]]s, and 1 [[regular hexagon]].{{r|berman}} The faces are all [[regular polygon]]s, categorizing the triangular hebesphenorotunda as a [[Johnson solid]], enumerated the last one <math> J_{92} </math>.{{r|francis}} It is an [[elementary polyhedra|elementary polyhedron]], meaning that it cannot be separated by a plane into two small regular-faced polyhedra.{{r|cromwell}}

The [[surface area]] of a triangular hebesphenorotunda of edge length <math> a </math> as:{{r|berman}}
<math display="block"> A = \left(3+\frac{1}{4}\sqrt{1308+90\sqrt{5}+114\sqrt{75+30\sqrt{5}}}\right)a^2 \approx 16.389a^2, </math>
and its [[volume]] as:{{r|berman}}
<math display="block"> V = \frac{1}{6}\left(15+7\sqrt{5}\right)a^3\approx5.10875a^3. </math>