# Stauromesohedron (EntityTopic, 11)

### From Hi.gher. Space

The **stauromesohedron** is also known as the **cuboctahedron**. Of the six uniform mesohedra, it is the only one whose elemental name is longer (by one syllable) than its widely accepted name, however it was renamed for consistency. t has 6 squares and 8 triangles as its faces, two of each kind of face join at each vertex.

## Equations

- The hypervolumes of a cuboctahedron are:

total edge length=24lsurface area= (6+2√3) ·l^{2}volume =^{5√2}∕_{3}·l^{3}## Incidence matrix

Dual: rhombic dodecahedron

# TXID Va Ea 3a 4a Type Name 0 Va = point ; 1 Ea 2 = digon ; 2 3a 3 3 = triangle ; 3 4a 4 4 = square ; 4 C1a 12 24 8 6 = stauromesohedron; ## Usage as facets

- 8× 1-facets of a D4.11
- 1× 1-facets of a bitrigonal diminished pyrocantichoron

Notable TrishapesRegular:tetrahedron • cube • octahedron • dodecahedron • icosahedron Direct truncates:tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate Mesotruncates:stauromesohedron• stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedronSnubs:snub staurohedron • snub rhodohedron Curved:sphere • torus • cylinder • cone • frustum • crind