7 Dimensional Shapes

Octaexon
An octaexon is a 7-dimensional simplex. It is also called the pyroexon under the elemental naming scheme.

Hypervolumes

 * vertex count = $$8$$
 * edge length = $$28l$$
 * surface area = $$14{ l }^{ 2 }\sqrt { 3 }$$
 * surcell volume = $$\frac { 35\sqrt { 3 } }{ 6 } { l }^{ 3 }$$
 * surteron bulk = $$\frac { 7\sqrt { 5 } }{ 12 } { l }^{ 4 }$$
 * surpeton pentavolume = $$\frac { 7\sqrt { 3 } }{ 120 } { l }^{ 5 }$$
 * surexon hexavolume = $$\frac { \sqrt { 7 } }{ 720 } { l }^{ 6 }$$
 * surzetton heptavolume = $$\frac { 1 }{ 20160 } { l }^{ 7 }$$

Subfacets

 * 8 points (0D)
 * 28 lines (1D)
 * 56 triangles (2D)
 * 70 tetrahedra (3D)
 * 56 pentachora (4D)
 * 28 hexatera (5D)
 * 8 heptapeta (6D)

7-orthoplex
A 7-orthoplex (heptarss) is a 7D shape. It is the seven-dimensional cross polytope.

Heptaphere
A heptaphere is a 7-dimensional hypersphere

Hepteract


The hepteract is the 7-hypercube.

Hypervolumes

 * vertex count =$$128$$
 * edge length =$$448l$$
 * surface area =$$670{ l }^{ 2 }$$
 * surcell volume =$$560{ l }^{ 3 }$$
 * surteron bulk =$$280{ l }^{ 4 }$$
 * surpeton pentavolume =$$84{ l }^{ 5 }$$
 * surecton hexavolume =$$14{ l }^{ 6 }$$
 * surzetton heptavolume =$${ l }^{ 7 }$$

Subfacets

 * 128 points (0D)
 * 448 line segments (1D)
 * 672 squares (2D)
 * 560 cubes (3D)
 * 280 tesseracts (4D)
 * 84 penteracts (5D)
 * 14 hexeracts (6D)