7 Dimensional Shapes

== Octaexon ==
An octaexon is a 7-dimensional simplex. It is also called the pyroexon under the elemental naming scheme.
===Properties===
====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)
Category:Shapes
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