Polygram (geometry)In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two triangles. A regular polygram {p/q} can either be in a set of regular star polygons (for gcd(p,q) = 1, q > 1) or in a set of regular polygon compounds (if gcd(p,q) > 1).
Ennéagramme (géométrie)In geometry, an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon. The word 'enneagram' combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆς (grammēs) meaning a line. A regular enneagram is a 9-sided star polygon. It is constructed using the same points as the regular enneagon, but the points are connected in fixed steps. Two forms of regular enneagram exist: One form connects every second point and is represented by the Schläfli symbol {9/2}.
Compound of dodecahedron and icosahedronIn geometry, this polyhedron can be seen as either a polyhedral stellation or a compound. It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It has icosahedral symmetry (Ih) and the same vertex arrangement as a rhombic triacontahedron. This can be seen as the three-dimensional equivalent of the compound of two pentagons ({10/2} "decagram"); this series continues into the fourth dimension as the compound of 120-cell and 600-cell and into higher dimensions as compounds of hyperbolic tilings.
Petit hécatonicosachore étoiléEn géométrie, le petit hécatonicosachore étoilé ou polydodécaèdre étoilé est un 4-polytope étoilé régulier ayant pour symbole de Schläfli {5/2,5,3}. C'est l'un des 10 polychores de Schläfli-Hess. Il a la même que l'hécatonicosachore 5,5/2,5 et partage également ses 120 sommets avec l'hexacosichore et huit autres polytopes réguliers étoilés. Il peut également être considéré comme la première stellation de l'hécatonicosichore. En ce sens, il pourrait être considéré comme analogue au petit dodécaèdre étoilé tridimensionnel, qui est la première stellation du dodécaèdre.
Excavated dodecahedronIn geometry, the excavated dodecahedron is a star polyhedron that looks like a dodecahedron with concave pentagonal pyramids in place of its faces. Its exterior surface represents the Ef1g1 stellation of the icosahedron. It appears in Magnus Wenninger's book Polyhedron Models as model 28, the third stellation of icosahedron. All 20 vertices and 30 of its 60 edges belong to its dodecahedral hull. The 30 other internal edges are longer and belong to a great stellated dodecahedron.
