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Polygons which have an accompanying imaginary dimension for each real dimension
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
Regular_complex_polygon
Polygon in complex space, or which self-intersects
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
Complex_polygon
Generalization of a polytope in real space
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
Complex_polytope
Plane figure bounded by line segments
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
Polygon
Polygonal chain whose vertices are not all coplanar
all coplanar, we speak of a plane polygon, otherwise a skew polygon." Regular complex polytopes, p. 6 Abstract Regular Polytopes, p.217 McMullen, Peter;
Skew_polygon
Skew polygon derived from a polytope
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
Petrie_polygon
Regular polygon that can be constructed with compass and straightedge
mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible
Constructible_polygon
Poset representing certain properties of a polytope
group, not the (geometric) symmetry group. For example, any abstract polygon is regular, since angles, edge-lengths, edge curvature, skewness etc. do not
Abstract_polytope
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
Möbius–Kantor_polygon
Method of drawing geometric objects
same area as a given polygon, and regular polygons of 3, 4, or 5 sides (or one with twice the number of sides of a given polygon). But they could not
Straightedge and compass construction
Straightedge_and_compass_construction
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
Approach to Discrete Math, Springer, p. 437, ISBN 9780387941158. Coxeter, Regular Complex Polytopes, second edition, p.114 Garey, Michael R.; Johnson, David
Complete_bipartite_graph
Pictorial representation of symmetry
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
Coxeter–Dynkin_diagram
Polygon shape with eight sides
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
Octagon
Four-dimensional analogues of the regular polyhedra in three dimensions
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
Regular_4-polytope
Polyhedron with regular congruent polygons as faces
A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron
Regular_polyhedron
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
3-3_duoprism
Polytope with highest degree of symmetry
themselves regular polytopes of dimension j≤ n. Regular polytopes are the generalised analog in any number of dimensions of regular polygons (for example
Regular_polytope
Points on a common circle
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
Concyclic_points
Shape with six sides
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
Hexagon
Non-planar polygon with infinitely many sides
M.; Regular complex polytopes (1974). Chapter 1. Regular polygons, 1.5. Regular polygons in n dimensions, 1.7. Zigzag and antiprismatic polygons, 1.8
Infinite_skew_polygon
Shape with four equal sides and angles
hyperbolic geometry both lack polygons with four equal sides and right angles, they have square-like regular polygons with four sides and other angles
Square
Four-dimensional analog of the octahedron
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
16-cell
Convex polyhedron with regular faces
a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not a uniform polyhedron. There are 92 such solids: 48
Johnson_solid
Sub-list of the list of polytopes
icositetragram, with twenty four edges 257-gram, with two hundred and fifty seven edges List of regular polytopes and compounds § Stars Complex polygon
List of self-intersecting polygons
List_of_self-intersecting_polygons
Extending the elements of a polytope to form a new figure
regular octahedron to obtain the stella octangula, a regular compound of two tetrahedra. Stellating a regular polygon symmetrically creates a regular
Stellation
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
List_of_regular_polytopes
Polygon with 65537 sides
a polygon with 65,537 (216 + 1) sides. The sum of the interior angles of any non-self-intersecting 65537-gon is 11,796,300°. The area of a regular 65537-gon
65537-gon
Regular object in four dimensional geometry
two from the northern hemisphere and two from the southern. The regular complex polygon 4{3}4, or contains the 24 vertices of the 24-cell, and 24 4-edges
24-cell
Number of times a curve wraps around a point in the plane
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
Winding_number
unchanged when rotated 180 degrees. The idea is also applicable for regular complex polygons, p{q}r constructed in C 2 {\displaystyle \mathbb {C} ^{2}} : [
Configuration_(polytope)
Geometric configuration of 9 points and 12 lines
\3&6\\\end{smallmatrix}}\right]} , which is represented in the regular complex polygon 3{4}2, 9 vertices and 6 3-edges. It is also the dual configuration
Hesse_configuration
Four-dimensional analog of the icosahedron
4-polytope and honeycombs with icosahedron vertex figures: The regular complex polygons 3{5}3, and 5{3}5, , in C 2 {\displaystyle \mathbb {C} ^{2}} have
600-cell
Geometric object with flat sides
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
Polytope
Concept in geometry
circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter multiplied by
Area_of_a_circle
Polygon with equally angled vertices
it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be
Equiangular_polygon
Decagram Hendecagram Dodecagram Icositetragram Concave polygon Cyclic polygon Regular polygon Polyform Gnomon Golygon List of uniform tilings Uniform
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Uniform 6-polytope
forming the 222 honeycomb with this Coxeter-Dynkin diagram: . The regular complex polygon 3{3}3{3}3, , in C 2 {\displaystyle \mathbb {C} ^{2}} has a real
2_21_polytope
Polygon associated with a compact Riemann surface
In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only information about
Fundamental_polygon
Point where two or more curves, lines, or edges meet
point where two lines meet to form an angle and the point where edges of polygons and polyhedra meet are vertices. The vertex of an angle is the point where
Vertex_(geometry)
Graph operation
value of the complex number. For 3-regular graphs this norm is the T-number or triangulation number used in virology. The master polygon is an equilateral
Goldberg–Coxeter_construction
Natural number
the first regular polygon that does not tile the plane with copies of itself. The pentagon solid has the largest face of any of the five regular three-dimensional
5
Abstract regular 4-polytope with 4 cubic cells
edges added. It is also the complete bipartite graph K4,4, and the regular complex polygon 2{4}4, a generalized cross polytope.[clarification needed] The
Hemitesseract
Flat-sided three-dimensional shape
vertex is regular. A vertex-transitive polyhedron with regular polygonal faces is said to be uniform. This class includes the regular, quasi-regular, and semi-regular
Polyhedron
Self-intersecting uniform polyhedron
either star polygon faces, star polygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra includes the 4 regular ones, called
Uniform_star_polyhedron
Set of basic shapes which assemble into a polygon
of a polygon is a set of primitive units (e.g., triangles, rectangles, etc.), which do not overlap and whose union equals the polygon. A polygon partition
Polygon_partition
Developer of the Petrie polygon
known as the "Petrie polygon" and has many applications. The Petrie polygon of a regular polyhedron can be defined as the skew polygon (whose vertices do
John_Flinders_Petrie
Texture mapping technique
by generating a normal map from a high polygon model or height map. Normal maps are commonly stored as regular RGB images where the RGB components correspond
Normal_mapping
Natural number
twelve-sided polygon is a dodecagon. In its regular form, it is the largest polygon that can uniformly tile the plane alongside other regular polygons, as with
12_(number)
Four-dimensional analog of the dodecahedron
of every convex regular polytope in the first four dimensions (except the polygons {7} and above). As the sixth and largest regular convex 4-polytope
120-cell
Simple curve of Euclidean geometry
side of the polygon. Every regular polygon and every triangle is a tangential polygon. A cyclic polygon is any convex polygon about which a circle can be
Circle
Four-dimensional analogue of the cube
of regular 4-polytope and honeycombs, {4,3,p} with cubic cells. The regular complex polytope 4{4}2, , in C 2 {\displaystyle \mathbb {C} ^{2}} has a real
Tesseract
Construction on any polygon that yields a regular polygon with the same number of sides
arbitrary planar polygons. The theorem asserts that a certain procedure when applied to an arbitrary polygon always yields a regular polygon having the same
Petr–Douglas–Neumann_theorem
Type of plane partition
Voronoi polygons, domain(s) of influence, Voronoi decomposition, Voronoi tessellation(s), Dirichlet tessellation(s). Voronoi tessellations of regular lattices
Voronoi_diagram
Solid with four equal triangular faces
regular Platonic solids—polyhedra in which all of their faces are regular polygons. Known since antiquity, Platonic solids are named after the Greek philosopher
Regular_tetrahedron
Property of objects which are scaled or mirrored versions of each other
condition for similarity of polygons is that corresponding sides and diagonals are proportional. For given n, all regular n-gons are similar. Several
Similarity_(geometry)
Circle associated with a quadratic equation
circles have been used to develop ruler-and-compass constructions of regular polygons. Given a quadratic equation in the form x2 − sx + p = 0 the circle
Carlyle_circle
Pentagon with all sides equal but the angles may not be equal
In geometry, an equilateral pentagon is a polygon in the Euclidean plane with five sides of equal length. Its five vertex angles can take a range of sets
Equilateral_pentagon
Natural number
number system. A polygon with eight sides is an octagon. A regular octagon can fill a plane-vertex with a regular triangle and a regular icositetragon,
8
Overview of and topical guide to geometry
problem Parallel postulate Polygon Star polygon Pick's theorem Shape dissection Bolyai–Gerwien theorem Poncelet–Steiner theorem Polygon triangulation Pons asinorum
Outline_of_geometry
polychoron Convex regular polychoron Duocylinder Tesseract Coxeter, H. S. M.; Regular Complex Polytopes, Cambridge University Press, (1974). Regular Polytopes
3-4_duoprism
the empty Schläfli symbol {}. Polygon Equilateral Cyclic polygon Convex polygon Star polygon Pentagram Regular polygon Equilateral triangle Simplex Square
List_of_mathematical_shapes
Number with a real and an imaginary part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary
Complex_number
Concept in differential equation mathematics
In mathematics, in the theory of ordinary differential equations in the complex plane C {\displaystyle \mathbb {C} } , the points of C {\displaystyle \mathbb
Regular_singular_point
Form of an object
include: Circle, Square, Triangle, Rectangle, Oval, Star (polygon), Rhombus, Semicircle. Regular polygons starting at pentagon follow the naming convention of
Shape
Polyhedron formed by joining mirroring pyramids base-to-base
regular polygon, the bipyramid is also called regular. A bipyramid is a polyhedron constructed by fusing two pyramids which share the same polygonal base;
Bipyramid
Convex polytope, the n-dimensional analogue of a square and a cube
vertex figure are regular simplexes. The regular polygon perimeter seen in these orthogonal projections is called a Petrie polygon. The generalized squares
Hypercube
Group of symmetries of a regular polygon
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among
Dihedral_group
Five tiles used in Islamic decorative art
An interlocking decagram-polygon mosaic design An interlocking decagram-polygon mosaic design An interlocking decagram-polygon mosaic design First, divide
Girih_tile
Study of complex manifolds and several complex variables
complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Feature of a polyhedron, polytope, etc.
authors call a facet of a polyhedron any polygon whose corners are vertices of the polyhedron, including polygons that are not faces. To facet a polyhedron
Facet_(geometry)
Solid with twenty equal triangular faces
The regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from a pentagonal antiprism by attaching two pentagonal
Regular_icosahedron
Solid with 12 equal pentagonal faces
of the Platonic solids, a set of polyhedrons in which the faces are regular polygons that are congruent and the same number of faces meet at a vertex. This
Regular_dodecahedron
Way to divide polygon into smaller parts
dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision rules in a sense are generalizations of regular geometric
Finite_subdivision_rule
Property of a mathematical space
Graph (combinatorics) Real number Length 2 dimensions Plane Surface Polygon Net Complex number Cartesian coordinate system List of uniform tilings Area 3
Dimension
Four-dimensional geometric object with flat sides
polygons and Kepler–Poinsot polyhedra. A 4-polytope is regular if it is transitive on its flags. This means that its cells are all congruent regular polyhedra
4-polytope
Geometric objects with a common centre
well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyhedra, parallelograms, cones, conic sections, and quadrics
Concentric_objects
quasirational polygon has all orbits bounded. The notion of quasirational is technical (see references) but it includes the class of regular polygons and convex
Outer_billiards
Set of principles for modeling solid geometry
customization) Creating polygon mesh models for rapid prototyping (to aid surgeons preparing for difficult surgeries, for example) Combining polygon mesh models with
Solid_modeling
Regular polytope dual to the hypercube in any number of dimensions
Petrie polygon projections map the points into a regular 2n-gon or lower order regular polygons. A second projection takes the 2(n−1)-gon petrie polygon of
Cross-polytope
Four-sided polygon
In geometry, a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words
Quadrilateral
Number, approximately 3.14
drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating
Pi
Tiling of a plane by regular hexagons and equilateral triangles
uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is
Trihexagonal_tiling
Type of polygon
In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufang planes studied by Ruth Moufang, and are irreducible buildings of rank
Moufang_polygon
Region between two concentric circles
A={\frac {\theta }{2}}\left(R^{2}-r^{2}\right).} In complex analysis an annulus ann(a; r, R) in the complex plane is an open region defined as r < | z − a
Annulus_(mathematics)
Branch of geometry that studies combinatorial properties and constructive methods
basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these
Discrete_geometry
symmetry as a regular complex polyhedron with 72 vertices, 216 3{} edges, 54 3{3}3 faces. Its vertex figure is 3{4}2, and van oss polygon 3{4}3. It is
Hessian_polyhedron
Partition of a polygon into triangles of equal area
question is: Which polygons can be equidissected into how many pieces? Particular attention has been given to trapezoids, kites, regular polygons, centrally symmetric
Equidissection
Data structure for representing polygon meshes in computer memory
contrast to simpler specifications of polygon meshes such as a node and element list, or the implied connectivity of a regular grid. An alternative to the winged
Winged_edge
3D computer graphics program
bind skinning option is useful for animating low-polygon models or as a diagnostic tool for regular skeleton animation. Additional modifiers, such as
Autodesk_3ds_Max
Final season of television series The Boys
can make a call. I lean on them a lot for that stuff", he explained to Polygon, adding: "We wanted a really distinct voice and who has a more distinct
The_Boys_season_5
6-dimensional hypercube
dimensions (n ≥ 5). ISBN 0-486-61480-8. Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2. Klitzing
6-cube
Relation between sides of a right triangle
a : b : c). While Euclid's proof only applied to convex polygons, the theorem also applies to concave polygons and even to similar figures that have curved boundaries
Pythagorean_theorem
7-dimensional hypercube
(iii): Regular Polytopes, three regular polytopes in n dimensions (n ≥ 5), ISBN 0-486-61480-8 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes
7-cube
Geometric structure of 8 points and 8 lines
the polygon vertices are complex numbers. Kantor's solution for p = 4 {\displaystyle p=4} , a pair of mutually-inscribed quadrilaterals in the complex projective
Möbius–Kantor_configuration
Mathematical instrument consisting of two hinged rulers
a "polymetric compass" c. 1670, including a scale for constructing regular polygons. The Italian astronomer Galileo Galilei added further scales in the
Sector_(instrument)
Regular tiling of a two-dimensional space
lattice Hexagonal prismatic honeycomb Tilings of regular polygons List of uniform tilings List of regular polytopes Hexagonal tiling honeycomb Hex map board
Hexagonal_tiling
Geometric model of the physical space
cylinder, or sphere. Book XIII describes the construction of the five regular Platonic solids in a sphere, covering the cube, octahedra, icosahedra and
Three-dimensional_space
Isogonal polytope with regular facets
identical meanings, because all uniform polygons must be regular. However, since not all uniform polyhedra are regular, the number of semiregular polytopes
Semiregular_polytope
Multi-dimensional generalization of triangle
the study of polytopes. These Petrie polygons (skew orthogonal projections) show all the vertices of the regular simplex on a circle, and all vertex pairs
Simplex
Smallest convex set containing a given set
convex hull of a simple polygon encloses the given polygon and is partitioned by it into regions, one of which is the polygon itself. The other regions
Convex_hull
REGULAR COMPLEX-POLYGON
REGULAR COMPLEX-POLYGON
Girl/Female
Bengali, Indian
Good Complex
Girl/Female
Muslim
One who remembers Allah regularly
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Girl/Female
Muslim/Islamic
One who remembers Allah regularly
Boy/Male
Tamil
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Girl/Female
Tamil
Complete
Girl/Female
Arabic, Muslim
Pilgrimage to Makkah Other than Regular Hajj Days
Boy/Male
Hindu, Indian, Traditional
Conduct; Regular Performance of Worship
Girl/Female
Hebrew
Precious.
Boy/Male
Indian, Sanskrit
Connector; Regulator
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Indian
One who remembers Allah regularly
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Boy/Male
Gujarati, Haryanvi, Hindu, Indian, Kannada, Marathi, Telugu
Regular; Ethical; Good in Nature
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Girl/Female
Hindu, Indian
Complex
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
REGULAR COMPLEX-POLYGON
REGULAR COMPLEX-POLYGON
Boy/Male
Hebrew
Gift from God.
Boy/Male
Hindu, Indian
Lord Murugan
Biblical
child of the Lord
Boy/Male
Tamil
Moons Love
Boy/Male
Egyptian English
Son.
Girl/Female
Australian, Danish, Dutch, German, Hebrew, Swedish
Life; Form of Eve
Girl/Female
Australian, French, Lebanese
Powerful
Boy/Male
Australian, French, Latin, Scottish
Christian
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, French, German, Latin
From Hadria; Dark
Surname or Lastname
English
English : from the personal name Wyun, a pet form of Old German Wido, Old French Guy.Americanized spelling of German Weiand, itself a variant of Wiegand.
REGULAR COMPLEX-POLYGON
REGULAR COMPLEX-POLYGON
REGULAR COMPLEX-POLYGON
REGULAR COMPLEX-POLYGON
REGULAR COMPLEX-POLYGON
a.
Intricate; entangled; complicated; complex.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
n.
A complex; an aggregate of parts; a complication.
a.
Not regular; not bound by monastic vows or rules; not confined to a monastery, or subject to the rules of a religious community; as, a secular priest.
a.
Repeatedly compound; made up of complex constituents.
a.
Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
a.
Thorough; complete; unmitigated; as, a regular humbug.
a.
Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.
adv.
In a complex manner; not simply.
imp. & p. p.
of Couple
a.
Not complex; uncompounded; simple.
a.
Complex, complicated.
pl.
of Tegula
a.
Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no straight; not uniform; as, an irregular line; an irregular figure; an irregular verse; an irregular physician; an irregular proceeding; irregular motion; irregular conduct, etc. Cf. Regular.
n.
One who is not regular; especially, a soldier not in regular service.
a.
Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.
imp. & p. p.
of Compile
pl.
of Regulus