# Octagonal prism (EntityTopic, 16)

### From Hi.gher. Space

## Equations

- The hypervolumes of an octagonal prism with side length
*l*are given by:

total edge length = 24l

surface area =l^{2}· 2(5 + √2)

volume =l^{3}· 2(1 + √2)

## Incidence matrix

Dual: octagonal bipyramid

# | TXID | Va | Ea | Eb | 4a | 8a | Type | Name |
---|---|---|---|---|---|---|---|---|

0 | Va | = point | ; | |||||

1 | Ea | 2 | = digon | ; | ||||

2 | Eb | 2 | = digon | ; | ||||

3 | 4a | 4 | 2 | 2 | = square | ; | ||

4 | 8a | 8 | 0 | 8 | = base of prism: octagon |
; | ||

5 | C1a | 16 | 8 | 16 | 8 | 2 | = octagonal prism |
; |

## Usage as facets

*This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.*

Notable Trishapes
| |

Regular:
| tetrahedron • cube • octahedron • dodecahedron • icosahedron |

Direct truncates:
| tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |

Mesotruncates:
| stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |

Snubs:
| snub staurohedron • snub rhodohedron |

Curved:
| sphere • torus • cylinder • cone • frustum • crind |