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Equiangular and equilateral polygon
regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons
Regular_polygon
Plane figure bounded by line segments
solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polygons and
Polygon
Regular non-convex polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not
Star_polygon
Subdivision of the plane into polygons that are all regular
Tilings of the Euclidean plane by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Polygon with 1 million edges
circle-like polygon with one million sides (mega-, from the Greek μέγας, meaning "great", being a unit prefix denoting a factor of one million). A regular megagon
Megagon
In geometry, an affine-regular polygon or affinely regular polygon is a polygon that is related to a regular polygon by an affine transformation. Affine
Affine-regular_polygon
Polygon with an infinite number of sides
apeiron 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case
Apeirogon
Mathematical term in geometry
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
Polygram_(geometry)
Limiting case which is different from the rest of the class
or at least one angle is 180°. Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides. In the case of triangles, this definition
Degeneracy_(mathematics)
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
Polygonal chain whose vertices are not all coplanar
even-sided. Regular skew polygons in 3 dimensions (and regular skew apeirogons in two dimensions) are always zig-zag. A regular skew polygon is a faithful
Skew_polygon
Shape with five sides
regular convex polygon, the regular convex pentagon has an inscribed circle. The apothem, which is the radius r of the inscribed circle, of a regular
Pentagon
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
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
Shape with nine sides
geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon. The name nonagon is a prefix hybrid formation, from Latin (nonus
Nonagon
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
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
Shape with three equal sides
of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle
Equilateral_triangle
Path that surrounds an area
perimeter of an equilateral polygon, one must multiply the common length of the sides by the number of sides. A regular polygon may be characterized by the
Perimeter
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
Polygon with 12 edges
In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. A regular dodecagon is a figure with sides of the same length and internal angles of
Dodecagon
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
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
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
Constant-width curve of equal-radius arcs
Reuleaux polygon. As a special case, this construction is possible for every regular polygon with an odd number of sides. Every Reuleaux polygon must have
Reuleaux_polygon
Any of the five regular polyhedra
polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number
Platonic_solid
Conic solid with a polygonal base
solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids)
Pyramid_(geometry)
Theorem on equilateral triangles
hexagon, which does not necessarily have opposite sides parallel. If a polygon is regular (both equiangular and equilateral), the sum of the distances to the
Viviani's_theorem
Polygon with 2 sides and 2 vertices
a representation of a graph with two vertices, see "Generalized polygon". A regular digon has both angles equal and both sides equal and is represented
Digon
Shape with seven sides
In geometry, a heptagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using septa- (an elision of septua-)
Heptagon
Polygon with 14 edges
a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon. A regular tetradecagon has Schläfli symbol {14} and can be constructed as a
Tetradecagon
Segment in a circle or sphere from its center to its perimeter or surface and its length
and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its vertices
Radius
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
In geometry a line segment joining two nonconsecutive vertices of a polygon or polyhedron
diagonals, and each diagonal is shared by two vertices. In general, a regular n-sided polygon has ⌊ n − 2 2 ⌋ {\displaystyle \left\lfloor {\frac {n-2}{2}}\right\rfloor
Diagonal
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
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
Polygon with 18 edges
an octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon. A regular octadecagon has a Schläfli symbol {18} and can be constructed as a
Octadecagon
Polygon with 20 edges
icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees. The regular icosagon has Schläfli symbol {20},
Icosagon
Polygon in which all sides have equal length
does then it is a regular polygon. If the number of sides is at least four, an equilateral polygon does not need to be a convex polygon: it could be concave
Equilateral_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
Measure of two radii meeting
the center of the circle is also the center of the polygon. The central angle of the regular polygon is formed at the center by the circumradii to two
Central_angle
Natural number
in its case only alongside a regular triangle and a 42-sided polygon (3.7.42). Otherwise, for any regular n-sided polygon, the maximum number of intersecting
7
Shape with eleven sides
hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and –gon "corner", is
Hendecagon
Polygon with 17 edges
a seventeen-sided polygon. A regular heptadecagon is represented by the Schläfli symbol {17}. As 17 is a Fermat prime, the regular heptadecagon is a constructible
Heptadecagon
Segment from the center of a polygon to the midpoint of one of its sides
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it
Apothem
Polygon with 10000 edges
10000-gon is a polygon with 10000 sides. Several philosophers have used the regular myriagon to illustrate issues regarding thought. A regular myriagon is
Myriagon
Polygon with 30 edges
thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 degrees. The regular triacontagon is a constructible polygon, by an edge-bisection
Triacontagon
Shape with ten sides
"ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A regular decagon has all sides of equal
Decagon
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)
Polygon with 1000 edges
distinct Fermat primes nor a power of two. Thus the regular chiliagon is not a constructible polygon. Indeed, it is not even constructible with the use
Chiliagon
Polygon with 13 edges
thirteen-sided polygon. A regular tridecagon is represented by Schläfli symbol {13}. The measure of each internal angle of a regular tridecagon is approximately
Tridecagon
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
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
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
Four-dimensional analogue of the cube
The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the
Tesseract
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
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
Covering by shapes without overlaps or gaps
special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one
Tessellation
Natural number
tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane. 42 is the
42_(number)
Type of figurate number
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate
Polygonal_number
Polygon with 24 edges
or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees. The regular icositetragon is represented by Schläfli
Icositetragon
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i
List_of_uniform_polyhedra
Non-planar polygon with infinitely many sides
A regular zig-zag skew apeirogon has (2*∞), D∞d Frieze group symmetry. Regular zig-zag skew apeirogons exist as Petrie polygons of the three regular tilings
Infinite_skew_polygon
Operation that cuts polytope vertices, creating a new facet in place of each vertex
regular polygon uniformly truncated will become another regular polygon: t{n} is {2n}. A complete truncation (or rectification), r{3}, is another regular polygon
Truncation_(geometry)
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
Polygon with 16 edges
(sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. A regular hexadecagon is a hexadecagon in which all angles are equal and all
Hexadecagon
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
German polymath and scholar (1777–1855)
proved the construction of the heptadecagon, the first progress in regular polygon construction in over 2000 years. He also introduced the concept of
Carl_Friedrich_Gauss
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
Concave polygon Constructible polygon Convex polygon Cyclic polygon Equiangular polygon Equilateral polygon Penrose tile Polyform Regular polygon Simple
List of two-dimensional geometric shapes
List_of_two-dimensional_geometric_shapes
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
Notation for polytopes and tessellations
p-sided regular polygon that is convex. For example, {3} is an equilateral triangle, {4} is a square, {5} a convex regular pentagon, etc. Regular star polygons
Schläfli_symbol
nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well. Polygons are primarily named by prefixes
List_of_polygons
Polygon with one edge and one vertex
by some as a polygon with one edge and one vertex. It has Schläfli symbol {1}. In Euclidean geometry a monogon is a degenerate polygon because its endpoints
Monogon
Convex polygon that contains an inscribed circle
triangles are tangential, as are all regular polygons with any number of sides. A well-studied group of tangential polygons are the tangential quadrilaterals
Tangential_polygon
Topics referred to by the same term
submersion Regular polygons, polygons with all sides and angles equal Regular polyhedron, a generalization of a regular polygon to higher dimensions Regular polytope
Regular
1884 novella by Edwin Abbott Abbott
Furthermore, the angle of an Isosceles Triangle or the number of sides of a (regular) Polygon may be altered during life by deeds or by surgery. An Equilateral Triangle
Flatland
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
Polytope or tiling whose vertices are identical
regular polygons, apeirogons and regular star polygons are isogonal. The dual of an isogonal polygon is an isotoxal polygon. Some even-sided polygons
Isogonal_figure
Archimedean solid with 62 faces
two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with
Rhombicosidodecahedron
Polygon with 257 sides
257-gon is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 45,900°. The area of a regular 257-gon is (with
257-gon
Full-sphere surround sound format
lie equally spaced on the circumference of a circle. The simplest Regular Polygon decoder is a Square with the listener in the centre. At least four
Ambisonics
Geometric figure which is "snugly enclosed" by another figure
inscribed in triangles or regular polygons, and triangles or regular polygons inscribed in circles. A circle inscribed in any polygon is called its incircle
Inscribed_figure
Solid with eight equal triangular faces
edges, and faces. A regular octahedron is one of the Platonic solids, a set of convex polyhedra whose faces are congruent regular polygons. Platonic solids
Regular_octahedron
Point on a line segment which is equidistant from both endpoints
Newton line. A regular polygon has an inscribed circle which is tangent to each side of the polygon at its midpoint. In a regular polygon with an even number
Midpoint
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
Solid with 2 parallel n-gonal bases connected by n parallelograms
In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of
Prism_(geometry)
Curved triangle with constant width
first of a sequence of Reuleaux polygons whose boundaries are curves of constant width formed from regular polygons with an odd number of sides. Some
Reuleaux_triangle
Polygon with 15 edges
pentakaidecagon or 15-gon is a fifteen-sided polygon. A regular pentadecagon is represented by Schläfli symbol {15}. A regular pentadecagon has interior angles of
Pentadecagon
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
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
Fractal creation method
i.e., ropt, for every N-sided regular polygon, that produces a fractal with optimal packing, i.e., the subscale polygons are in contact but do not overlap
Chaos_game
Polygon with 23 sides
a 23-sided polygon. The icositrigon has the distinction of being the smallest regular polygon that is not neusis constructible. A regular icositrigon
Icositrigon
Perimeter of a circle or ellipse
circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides increases without bound. The term circumference
Circumference
Half of the sum of side lengths of a polygon
In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears
Semiperimeter
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)
Special n-gon that has the largest area among all diameter-one n-gons
when n = 4 {\displaystyle n=4} is a square, and the solution is a regular polygon when n {\displaystyle n} is an odd number, but the solution is irregular
Biggest_little_polygon
Curve traced by a vertex of a polygon as it rolls
In geometry, a cyclogon is the curve traced by a vertex of a regular polygon that rolls without slipping along a straight line. In the limit, as the number
Cyclogon
Star polygon
general, an octagram is any self-intersecting octagon (8-sided polygon). The regular octagram is labeled by the Schläfli symbol {8/3}, which means an
Octagram
REGULAR POLYGON
REGULAR POLYGON
Male
Spanish
Spanish form of Roman Latin Regulus, RÉGULO means "ruler."
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' Edward Poins, an irregular humorist.
Girl/Female
Hebrew
Precious.
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Surname or Lastname
North German
North German : variant of Asch.English : variant spelling of Ash (asche was the regular Middle English spelling of this word).
Boy/Male
Indian, Sanskrit
Connector; Regulator
Boy/Male
Hindu, Indian, Traditional
Conduct; Regular Performance of Worship
Male
Italian
Italian form of German Reginar, RANIERO means "wise warrior."
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' An irregular humorist.
Girl/Female
Muslim/Islamic
One who remembers Allah regularly
Surname or Lastname
English (Devon)
English (Devon) : unexplained. Possibly an irregular variant of Birchall.
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bowen, with the addition of the regular English patronymic suffix -s.Altered spelling of Dutch Bouwens, a variant of Bauwens.
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bevan, with the addition of the regular English patronymic suffix -s.
Girl/Female
Arabic, Muslim
Pilgrimage to Makkah Other than Regular Hajj Days
Surname or Lastname
English
English : nickname probably for a tenant whose feudal obligations included a regular payment in cash or kind (for example bread or salt) of a halfpenny.
Girl/Female
Muslim
One who remembers Allah regularly
Male
Scandinavian
Scandinavian form of German Reginar, RAGNAR means "wise warrior."
Male
German
A derivative of German Reginar, RAINER means "wise warrior."
Boy/Male
Gujarati, Haryanvi, Hindu, Indian, Kannada, Marathi, Telugu
Regular; Ethical; Good in Nature
Girl/Female
Indian
One who remembers Allah regularly
REGULAR POLYGON
REGULAR POLYGON
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
An Excellent Warrior; King
Girl/Female
Indian
Pretty; Holy Message of Saint; Cleaver
Girl/Female
Tamil
Manishka | மாஂநீஷà¯à®•à®¾
Wisdom, Intellect
Girl/Female
Hindu
Another name for Goddess Durga
Girl/Female
American, British, English
Free; Variant of Frances
Girl/Female
Tamil
Beauty, Pretty
Girl/Female
Arabic, Muslim
Patience; Perseverance
Boy/Male
Hindu, Indian
Lord Vishnu
Boy/Male
Muslim
Servant of the gatherer
Surname or Lastname
English (Devon)
English (Devon) : variant of Prue.Americanized spelling of German and Jewish Preuss.
REGULAR POLYGON
REGULAR POLYGON
REGULAR POLYGON
REGULAR POLYGON
REGULAR POLYGON
adv.
In a regular manner; in uniform order; methodically; in due order or time.
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.
a.
Of or pertaining to a tile; resembling a tile, or arranged like tiles; consisting of tiles; as, a tegular pavement.
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.
pl.
of Regulus
n.
One who is not regular; especially, a soldier not in regular service.
pl.
of Tegula
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.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
a.
Of or pertaining to the jugular vein; as, the jugular foramen.
n.
A secular ecclesiastic, or one not bound by monastic rules.
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
n. pl.
A division of Echini which includes the circular, or regular, sea urchins.
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.
a.
Thorough; complete; unmitigated; as, a regular humbug.
a.
Irregular in position; having no regular order; as, scattered leaves.
v. t.
To cause to become regular; to regulate.
a.
Measured by an angle; as, angular distance.
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.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.