Octagram
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Octagram | |
---|---|
Rank | 2 |
Type | Regular |
Notation | |
Bowers style acronym | Og |
Coxeter diagram | x8/3o () |
Schläfli symbol | {8/3} |
Elements | |
Edges | 8 |
Vertices | 8 |
Vertex figure | Dyad, length √2–√2 |
Measures (edge length 1) | |
Circumradius | |
Inradius | |
Area | |
Angle | 45° |
Central density | 3 |
Number of external pieces | 16 |
Level of complexity | 2 |
Related polytopes | |
Army | Oc, edge length |
Dual | Octagram |
Conjugate | Octagon |
Convex core | Octagon |
Abstract & topological properties | |
Flag count | 16 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(8), order 16 |
Convex | No |
Nature | Tame |
The octagram is a non-convex polygon with 8 sides. It's created by stellating the octagon. A regular octagram has equal sides and equal angles.
This is the second stellation of the octagon, and the only one that is not a compound. The only other polygons with a single non-compound stellation are the pentagon, the decagon, and the dodecagon.
The octagram is the uniform quasitruncation of the square, and as such is the only regular star polygon to regularly appear in non-prismatic uniform polytopes in 5 dimensions and higher.
Vertex coordinates[edit | edit source]
Coordinates for an octagram of unit edge length, centered at the origin, are all permutations of
Representations[edit | edit source]
An octagram has the following Coxeter diagrams:
- x8/3o (full symmetry)
- x4/3x () (B2 symmetry)
Related polytopes[edit | edit source]
The Octagram is one of 12 regular octagons in Euclidean space.
Name | Extended Schläfli symbol | Dimensions |
---|---|---|
octagon | 2 | |
octagram | 2 | |
octagonal-square coil | 4 | |
octagonal-octagrammic coil | 4 | |
skew octagon | 3 | |
square-octagrammic coil | 4 | |
skew octagram | 3 | |
octagonal-square-octagrammic coil | 6 | |
skew octagonal-square coil | 5 | |
skew octagonal-octagrammic coil | 5 | |
skew square-octagrammic coil | 5 | |
skew octagonal-square-octagrammic coil | 7 |
External links[edit | edit source]
- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".
- Klitzing, Richard. "Polygons"
- Wikipedia contributors. "Octagram".
- Hartley, Michael. "{8}*16".