Pentachoron

A pentachoron is a 4-dimensional simplex. It is also called the pyrochoron under the elemental naming scheme. Its Bowers acronym is "pen".

Structure
The pentachoron is the pyramid on the tetrahedron, with 4 tetrahedra on each vertex.

Hypervolumes

 * vertex count = $$5$$
 * edge length = $$10l$$
 * surface area = $$\frac { 5\sqrt { 3 }  }{ 2 } { l }^{ 2 }$$
 * surcell volume = $$\frac { \sqrt { 2 } }{ 3 } { l }^{ 3 }$$
 * surteron bulk = $$\frac { \sqrt { 5 } }{ 96 } { l }^{ 4 }$$

Subfacets

 * 5 points (0D)
 * 10 lines (1D)
 * 10 triangles (2D)
 * 5 tetrahedra (3D)