Compound of two hexagons
(Redirected from Stellated dodecagon)
Compound of two hexagons | |
---|---|
Rank | 2 |
Type | Regular |
Notation | |
Bowers style acronym | Sedog |
Schläfli symbol | {12/2} |
Elements | |
Components | 2 hexagons |
Edges | 12 |
Vertices | 12 |
Vertex figure | Dyad, length √3 |
Measures (edge length 1) | |
Circumradius | 1 |
Inradius | |
Area | |
Angle | 120° |
Central density | 2 |
Number of external pieces | 24 |
Level of complexity | 2 |
Related polytopes | |
Army | Dog, edge length |
Dual | Compound of two hexagons |
Conjugate | Compound of two hexagons |
Convex core | Dodecagon |
Abstract & topological properties | |
Flag count | 24 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(12), order 24 |
Convex | No |
Nature | Tame |
The stellated dodecagon, or sedog, is a polygon compound composed of two hexagons. As such it has 12 edges and 12 vertices.
As the name suggests, it is the first stellation of the dodecagon.
Its quotient prismatic equivalent is the hexagonal antiprism, which is three-dimensional.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a stellated dodecagon of edge length 1 centered at the origin are given by:
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Variations[edit | edit source]
The stellated dodecagon can be varied by changing the angle between the two component hexagons from the usual 30°. These 2-hexagon compounds generally have a dihexagon as their convex hull and remain uniform, but not regular, with hexagonal symmetry only.
External links[edit | edit source]
- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".