In geometry, a regular complex polygon is a generalization of a regular polygon in real space to an analogous structure in a complex Hilbert space, where...

graphics, a polygon whose boundary is not simple. In geometry, a complex polygon is a polygon in the complex Hilbert plane, which has two complex dimensions...

Hilbert plane consisting of two complex dimensions. Star polygon: a polygon which self-intersects in a regular way. A polygon cannot be both a star and star-shaped...

points lie at the vertices of a regular polygon centered on the origin. Three real projections of regular complex polygon 4{4}2 are illustrated above, with...

group, not the (geometric) symmetry group. For example, any abstract polygon is regular, since angles, edge-lengths, edge curvature, skewness etc. do not...

mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible...

the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive...

Coxeter 1973, §1.1 Regular polygons; "If the vertices are all coplanar, we speak of a plane polygon, otherwise a skew polygon." Regular complex polytopes, p...

In geometry, the Möbius–Kantor polygon is a regular complex polygon 3{3}3, , in C 2 {\displaystyle \mathbb {C} ^{2}} . 3{3}3 has 8 vertices, and 8 edges...

a regular polygon. The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is...

it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be...

Greek ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as...

and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. The convex regular 4-polytopes...

Approach to Discrete Math, Springer, p. 437, ISBN 9780387941158. Coxeter, Regular Complex Polytopes, second edition, p.114 Garey, Michael R.; Johnson, David...

A regular complex polygon in C 2 {\displaystyle \mathbb {C} ^{2}} , has the form p{q}r or Coxeter diagram . The symmetry group of a regular complex polygon...

themselves regular polytopes of dimension j≤ n. Regular polytopes are the generalised analog in any number of dimensions of regular polygons (for example...

be seen as its dual, a 4-4 duopyramid. The Möbius–Kantor polygon is a regular complex polygon 3{3}3, , in C 2 {\displaystyle \mathbb {C} ^{2}} shares the...

icositetragram, with twenty four edges 257-gram, with two hundred and fifty seven edges List of regular polytopes and compounds § Stars Complex polygon...

A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron...

area as a given polygon, and regular polygons of 3, 4, or 5 sides: p. xi  (or one with twice the number of sides of a given polygon: pp. 49–50 ). But...

M.; Regular complex polytopes (1974). Chapter 1. Regular polygons, 1.5. Regular polygons in n dimensions, 1.7. Zigzag and antiprismatic polygons, 1.8...

Every regular polygon is a cyclic polygon. For a cyclic polygon with an odd number of sides, all angles are equal if and only if the polygon is regular. A...

an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In...

angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. A regular hexagon is defined as...

hyperbolic geometry both lack polygons with four equal sides and right angles, they have square-like regular polygons with four sides and other angles...

connecting non-adjacent vertices of a regular polygon, these shapes range from simple three-pointed stars to more complex forms like the Heptagram and Enneagram...

connecting all pairs, just like a 5-simplex seen in projection. The regular complex polygon 2{4}3, also 3{ }+3{ } has 6 vertices in C 2 {\displaystyle \mathbb...

problem Parallel postulate Polygon Star polygon Pick's theorem Shape dissection Bolyai–Gerwien theorem Poncelet–Steiner theorem Polygon triangulation Pons asinorum...

the density is 1, by the Jordan curve theorem. By contrast, for a regular star polygon {p/q}, the density is q. Turning number cannot be defined for space...

regular compound of two tetrahedra. Stellating a regular polygon symmetrically creates a regular star polygon or polygonal compound. These polygons are...