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

## Properties

### 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 = $\frac { \sqrt { 5 } }{ 96 } { l }^{ 4 }$