10 Dimensional Shapes

Decarss

A Decarss is the ten-dimensional cross polytope. It is the dual of the dekeract and has a schläfli symbol of $\{3,3,3,3,3,3,3,3,4\}$.

Dekeract

Dekeract is the 10-hypercube.

Hypervolumes

• vertex count = $1024$
• edge length = $5120l$
• surface area = $11520{ l }^{ 2 }$
• surcell volume = $15360{ l }^{ 3 }$
• surteron bulk = $13440{ l }^{ 4 }$
• surpeton pentavolume = $8064{ l }^{ 5 }$
• surecton hexavolume = $3360{ l }^{ 6 }$
• surzetton heptavolume = $960{ l }^{ 7 }$
• suryotton octavolume = $180{ l }^{ 8 }$
• surxennon enneavolume = $20{ l }^{ 9 }$
• surdakon decavolume = ${ l }^{ 10 }$

Subfacets

• 1024 points (0D)
• 5120 line segments (1D)
• 11520 squares (2D)
• 15360 cubes (3D)
• 13440 tesseracts (4D)
• 8064 penteracts (5D)
• 3360 hexeracts (6D)
• 960 hepteracts (7D)
• 180 octeracts (8D)
• 20 enneracts (9D)

Hendecaxennon

The hendecaxennon is the 10-dimensional simplex. It is also known as the pyroxennon under the elemental naming scheme.

Subfacets

• 11 points (0D)
• 55 line segments (1D)
• 165 triangles (2D)
• 330 tetrahedra (3D)
• 462 pentachora (4D)
• 462 hexatera (5D)
• 330 heptapeta (6D)
• 165 octaexa (7D)
• 55 enneazetta (8D)
• 11 decayotta (9D)