Trigonal trioprism

Trigonal trioprism
Dimensionality	6
Schläfli Symbol	'"`UNIQ--postMath-00000008-QINU`"'
Subfacets
Vertices	27 points
Edges	81 line segments
Faces	81 squares 27 triangles
Cells	27 cubes 54 triangular prisms
Tera	27 trigonal-square duoprisms 9 trigonal duoprisms
Peta	9 trigonal duoprism prism
Ecta	1 trigonal trioprism
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000001-QINU`"'
Edge Length	'"`UNIQ--postMath-00000002-QINU`"'
Surface Area	'"`UNIQ--postMath-00000003-QINU`"'
Surcell Volume	'"`UNIQ--postMath-00000004-QINU`"'
Surteron Bulk	'"`UNIQ--postMath-00000005-QINU`"'
Surpeton Pentavolume	'"`UNIQ--postMath-00000006-QINU`"'
Surecton Hexavolume	'"`UNIQ--postMath-00000007-QINU`"'

A trigonal trioprism is the six-dimensional cartesian product of three triangles. Its Bowers' acronym is trittip. It can be considered as the cube of the triangle.

Structure and Sections

The sections of this shape fromm one of the facets look the same: a trigonal duoprismatic prism shrinking to a trigonal duoprism.

Hypervolumes

• vertex count = $27$
• edge length = $81 l$
• surface area = $\left( 81 + \frac{27\sqrt{3}}{4} \right) l^2$
• surcell volume = $\left( 27 + \frac{27\sqrt{3}}{2} \right) l^3$
• surteron bulk = $\left( \frac{27}{16} + \frac{27\sqrt{3}}{4} \right) l^4$
• surpeton pentavolume = $\frac{27}{16} l^5$
• surecton hexavolume = $\frac{3\sqrt{3}}{64} l^6$

Subfacets

• 27 points (0D)
• 81 line segments (1D)
• 81 squares (2D)
• 27 triangles (2D)
• 27 cubes (3D)
• 54 triangular prisms (3D)
• 27 trigonal-square duoprisms (4D)
• 9 trigonal duoprisms (4D)
• 9 trigonal duoprism prism (5D)
• 1 trigonal trioprism (6D)