Dodecagonal prism

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Dodecagonal prism
Rank3
TypeUniform
Notation
Bowers style acronymTwi
Coxeter diagramx2x12o ()
Conway notationP12
Elements
Faces12 squares, 2 dodecagons
Edges12+24
Vertices24
Vertex figureIsosceles triangle, edge lengths 2, 2, 2+3
Measures (edge length 1)
Circumradius
Volume
Dihedral angles4–4: 150°
 4–12: 90°
Height1
Central density1
Number of external pieces14
Level of complexity3
Related polytopes
ArmyTwip
RegimentTwip
DualDodecagonal tegum
ConjugateDodecagrammic prism
Abstract & topological properties
Flag count144
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
SkeletonGP(12,1)
Properties
SymmetryI2(12)×A1, order 48
ConvexYes
NatureTame

The dodecagonal prism, or twip, is a prismatic uniform polyhedron. It consists of 2 dodecagons and 12 squares. Each vertex joins one dodecagon and two squares. As the name suggests, it is a prism based on a dodecagon.

Vertex coordinates[edit | edit source]

A dodecagonal prism of edge length 1 has vertex coordinates given by:

  • ,
  • ,
  • .

Representations[edit | edit source]

A dodecagonal prism has the following Coxeter diagrams:

Semi-uniform variant[edit | edit source]

The dodecagonal prism has a semi-uniform variant of the form x y12o that maintains its full symmetry. This variant uses rectangles as its sides.

With base edges of length a and side edges of length b, its circumradius is given by and its volume is given by .

A decagonal prism with base edges of length a and side edges of length b can be alternated to form a hexagonal antiprism with base edges of length and side edges of lengths . In particular if the side edges are times the length of the base edges this gives a uniform pentagonal antiprism.

Variations[edit | edit source]

A dodecagonal prism has the following variations:

External links[edit | edit source]