Triangular octagoltriate (EntityTopic, 11)

From Higher Dimensions Database

The triangular octagoltriate is a powertope formed by taking the octagon of the triangle. It is therefore the convex hull of two ditriangular duoprisms, each being the duoprism of triangles of side 1 and 1+√2, oriented in opposite axes.

Cells

The triangular octagoltriate has the following cells:

  • prism of side 1+√2 and end equilateral triangle of side 1
  • antifrustoid of base rectangle of sides 1 and 1+√2 and unknown height

Faces

The triangular octagoltriate has the following faces:

  • 6× equilateral triangle of side 1
  • 18× rectangle of sides 1 and 1+√2
  • 18× trapezium of base 1+√2, height √3 and apex ½√6+√3

Incidence matrix

Dual: (dual of triangular octagoltriate)

#TXIDVaEaEbEc3a4a4bC1aC2aTypeName
0 Va = point ;
1 Ea 2 = digon ; edges on small triangles
2 Eb 2 = digon ; edges on large (internal) triangles
3 Ec 2 = digon ; edges joining small to large
4 3a 3300 = triangle ; small triangles
5 4a 4220 = square ; rectangles in prisms
6 4b 4112 = square ; trapeziums in antifrustoids
7 C1a 6630230 = triangular prism ; prisms
8 C2a 8444024 = cube ; antifrustoids
9 H4.1a 18181896181869 = triangular octagoltriate ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonediconeconinder
Torii: tigertorispherespheritorustorinderditorus