Hexagonal trioprism

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Hexagonal trioprism
Rank6
TypeUniform
Notation
Bowers style acronymHittip
Coxeter diagramx6o x6o x6o
Elements
Peta18 hexagonal duoprismatic prisms
Tera108 square-hexagonal duoprisms, 18 hexagonal duoprisms
Cells216 cubes, 216 hexagonal prisms
Faces648 squares, 108 hexagons
Edges648
Vertices216
Vertex figureDigonal trisphenoid
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dipetal anglesHahip–hiddip–hahip: 120°
 Hahip–shiddip–hahip: 90°
Central density1
Number of external pieces18
Level of complexity15
Related polytopes
ArmyHittip
RegimentHittip
DualHexagonal triotegum
ConjugateHexagonal trioprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryG2≀S3, order 10368
ConvexYes
NatureTame

The hexagonal trioprism or hittip is a convex uniform trioprism that consists of 18 hexagonal duoprismatic prisms as facets. 6 facets join at each vertex. It is also the 18-5-7 gyropeton.

This polypeton can be alternated into a triangular trioantiprism, although it cannot be made uniform.

The hexagonal trioprism can be vertex-inscribed into the rectified pentacontatetrapeton.

Vertex coordinates[edit | edit source]

The vertices of a hexagonal trioprism of edge length 1 are given by:

External links[edit | edit source]