6 Dimensional Shapes

Heptapeton
A heptapeton is a 6-dimensional simplex. It is also called the pyropeton under the elemental naming scheme.

Hypervolumes

 * vertex count = $$7$$
 * edge length = $$21l$$
 * surface area = $$\frac { 35\sqrt { 3 }  }{ 4 } { l }^{ 2 }$$
 * surcell volume = $$\frac { 35\sqrt { 3 } }{ 12 } { l }^{ 3 }$$
 * surteron bulk = $$\frac { 7\sqrt { 5 } }{ 32 } { l }^{ 4 }$$
 * surpeton pentavolume = $$\frac { 7\sqrt { 3 } }{ 480 } { l }^{ 5 }$$
 * surexon hexavolume = $$\frac { \sqrt { 7 } }{ 5760 } { l }^{ 6 }$$

Subfacets

 * 7 points (0D)
 * 21 lines (1D)
 * 35 triangles (2D)
 * 35 tetrahedra (3D)
 * 21 pentachora (4D)
 * 7 hexatera (5D)

Hexeract


A Hexeract is a 6-dimensional hypercube.

Hypervolumes

 * vertex count =$$64$$
 * edge length =$$192l$$
 * surface area =$$240{ l }^{ 2 }$$
 * surcell volume =$$160{ l }^{ 3 }$$
 * surteron bulk =$$60{ l }^{ 4 }$$
 * surpeton pentavolume =$$12{ l }^{ 5 }$$
 * surecton hexavolume =$${ l }^{ 6 }$$

Subfacets

 * 64 points (0D)
 * 192 line segment (1D)
 * 240 squares (2D)
 * 160 cubes (3D)
 * 60 tesseracts (4D)
 * 12 penteracts (5D)

6-orthoplex
A 6-orthoplex (Hexarss) is the six-dimensional cross polytope. It is the dual of the hexeract and has a schläfli symbol of $$\{3,3,3,3,4\}$$.

Subfacets

 * 12 points (0D)
 * 60 line segments (1D)
 * 160 triangles (2D)
 * 240 tetrahedrons (3D)
 * 192 tetrarsses (4D)
 * 64 pentarsses (5D)

Hexaphere
A hexaphere is the 6-dimensional hypersphere.

Hypervolumes

 * vertex count = $$N/A$$
 * edge length = $$N/A$$
 * surface area = $$N/A$$
 * surcell volume = $$N/A$$
 * surteron bulk = $$N/A$$
 * surpeton pentavolume = $$\frac { { \pi }^{ 3 } }{ 32 } { l }^{ 5 }$$
 * surecton hexavolume = $$\frac { { \pi  }^{ 3 } }{ 384 } l^{ 6 }$$