In geometry, an octagram is an eight-angled star polygon.
The name octagram combine a Greek numeral prefix, octa-, with the Greek suffix -gram. The -gram suffix derives from γραμμή (grammḗ) meaning "line".[1]
In general, an octagram is any self-intersecting octagon (8-sided polygon).
The regular octagram is labeled by the Schläfli symbol, which means an 8-sided star, connected by every third point.
These variations have a lower dihedral, Dih4, symmetry:
The symbol Rub el Hizb is a Unicode glyph ۞ at U+06DE.
Deeper truncations of the square can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices and two edge lengths. A truncated square is an octagon, t=. A quasitruncated square, inverted as, is an octagram, t=.[2]
The uniform star polyhedron stellated truncated hexahedron, t'=t has octagram faces constructed from the cube in this way. It may be considered for this reason as a three-dimensional analogue of the octagram.
Another three-dimensional version of the octagram is the nonconvex great rhombicuboctahedron (quasirhombicuboctahedron), which can be thought of as a quasicantellated (quasiexpanded) cube, t0,2.
There are two regular octagrammic star figures (compounds) of the form, the first constructed as two squares =2, and second as four degenerate digons, =4. There are other isogonal and isotoxal compounds including rectangular and rhombic forms.
or 2, like Coxeter diagrams +, can be seen as the 2D equivalent of the 3D compound of cube and octahedron, +, 4D compound of tesseract and 16-cell, + and 5D compound of 5-cube and 5-orthoplex; that is, the compound of a n-cube and cross-polytope in their respective dual positions.An octagonal star can be seen as a concave hexadecagon, with internal intersecting geometry erased. It can also be dissected by radial lines.