Hendecagrammic-great hendecagrammic duoprism

From Polytope Wiki
Revision as of 02:57, 15 November 2023 by The New Kid (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
Hendecagrammic-great hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/3o x11/4o ()
Elements
Cells11 hendecagrammic prisms, 11 great hendecagrammic prisms
Faces121 squares, 11 hendecagrams, 11 great hendecagrams
Edges121+121
Vertices121
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/11) (base 1), 2cos(4π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesShenp–4–gishenp: 90°
 Gishenp–11/4–gishenp:
 Shenp–11/3–shenp:
Central density12
Number of external pieces44
Level of complexity24
Related polytopes
ArmySemi-uniform handip
DualHendecagrammic-great hendecagrammic duotegum
ConjugatesHendecagonal-small hendecagrammic duoprism, Hendecagonal-hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count2904
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)×I2(11), order 484
ConvexNo
NatureTame

The hendecagrammic-great hendecagrammic duoprism, also known as the 11/3-11/4 duoprism, is a uniform duoprism that consists of 11 hendecagrammic prisms and 11 great hendecagrammic prisms, with 2 of each at each vertex.

The name can also refer to the small hendecagrammic-great hendecagrammic duoprism, the great hendecagrammic duoprism, or the great hendecagrammic-grand hendecagrammic duoprism.

Coordinates[edit | edit source]

The vertex coordinates of a hendecagrammic-great hendecagrammic duoprism, centered at the origin and with edge length 4sin(3π/11)sin(4π/11), are given by:

  • ,
  • ,
  • ,
  • ,

where j, k = 2, 4, 6, 8, 10.

External links[edit | edit source]