Dodecagon

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Dodecagon
Regular dodecagon.svg
Rank2
TypeRegular
SpaceSpherical
Bowers style acronymDog
Info
Coxeter diagramx12o
Schläfli symbol{12}
SymmetryI2(12), order 24
ArmyDog
Elements
Vertex figureDyad, length (2+6)/2
Edges12
Vertices12
Measures (edge length 1)
Circumradius
Inradius
Area
Angle150°
Central density1
Euler characteristic0
Number of pieces12
Level of complexity1
Related polytopes
DualDodecagon
ConjugateDodecagram
Properties
ConvexYes
OrientableYes
NatureTame

The dodecagon, or dog, is a polygon with 12 sides. A regular dodecagon has equal sides and equal angles.

The combining prefix is twa-, as in twaddip.

The only non-compound stellation of the dodecagon is the dodecagram. This makes it the largest polygon with a single non-compound stellation. The only other polygons with only one are the pentagon, the octagon, and the decagon.

Regular dodecagons dgenerally do not occur in higher spherical polytopes aside from prisms, though some Euclidean tilings with hexagonal tiling symmetry do use dodecagonal faces.

Naming[edit | edit source]

The name decagon is derived from the Ancient Greek δώδεκα (12) and γωνία (angle), referring to the number of vertices.

Other names include:

  • dog, Bowers style acronym, short for "dodecagon"

Vertex coordinates[edit | edit source]

Coordinates for a dodecagon of unit edge length, centered at the origin, are all permutations of:

Representations[edit | edit source]

A dodecagon has the following Coxeter diagrams:

  • x12o (full symmetry)
  • x6x (G2 symmetry, generally a dihexagon)
  • xy3yx&#zx (A2 symmetry, y = 1+√3)

Variations[edit | edit source]

Two main variants of the dodecagon have hexagon symmetry: the dihexagon, with two alternating side lengths and equal angles, and the dual hexambus, with two alternating angles and equal edges. Other less regular variations with square, triangular, rectangular, mirror, or no symmetry also exist.

Stellations[edit | edit source]

External links[edit | edit source]