7 Dimensional Shapes

octaexon

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

7-orthoplex
Geometry
Dimensionality	7D
Schläfli Symbol	{4,3,3,3,3,3}

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)