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Simple polygon which is not convex
A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that
Concave_polygon
Regular non-convex polygon
concave simple polygons. Polygrams include polygons like the pentagram, but also compound figures like the hexagram. One definition of a star polygon
Star_polygon
Polygon in which all sides have equal length
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 or even self-intersecting
Equilateral_polygon
Plane figure bounded by line segments
that passes outside the polygon. Simple: the boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple
Polygon
Negative of a convex function
including phase separation will be non-strictly concave. Concave polygon Jensen's inequality Logarithmically concave function Quasiconcave function Concavification
Concave_function
Set of polygons to define the surface of a 3D model
convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes. The study of polygon meshes
Polygon_mesh
Polygon that is the boundary of a convex set
triangle is strictly convex. Convex curve – Type of plane curve Concave polygon – Simple polygon which is not convex Convex polyhedron – Polyhedron that is
Convex_polygon
Polygon in which all angles are right
number of concave corners. To see why, imagine that you traverse the boundary of the polygon clockwise (with your right hand inside the polygon and your
Rectilinear_polygon
Topics referred to by the same term
Concave function, the negative of a convex function Concave polygon, a polygon which is not convex Concave set The concavity of a function, determined by its
Concave
Algorithm for clipping polygons
single polygon that is entirely visible. Note that if the subject polygon was concave at vertices outside the clipping polygon, the new polygon may have
Sutherland–Hodgman_algorithm
In geometry, set whose intersection with every line is a single line segment
non-convex set. A polygon that is not a convex polygon is sometimes called a concave polygon, and some sources more generally use the term concave set to mean
Convex_set
Supplementary pair of angles at each vertex of a polygon
the polygon. In other words, the sum of all the exterior angles is 2πk radians or 360k degrees. Example: for ordinary convex polygons and concave polygons
Internal_and_external_angles
Balbis 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
Property of a planar simple closed curve
concavity. For example, in the polygon pictured above, if we wanted to know whether the sequence of points F-G-H is concave, convex, or collinear (flat)
Curve_orientation
Polytope or tiling with one type of edge
{\displaystyle {\color {royalblue}^{\mathsf {o}}},} making convex or concave polygons respectively. A star 2 n {\displaystyle {\color {royalblue}{\mathbf
Isotoxal_figure
Graphics software library
concave or self-intersecting. Contours may be nested. In other words, polygons may have holes. The clip operation output from GPC is a set of polygon
General_Polygon_Clipper
Enneagram 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
Partition of a simple polygon into triangles
algorithms, and it only works on polygons without holes. An implementation that keeps separate lists of convex and concave vertices will run in O(n2) time
Polygon_triangulation
Polyhedron formed by joining mirroring pyramids base-to-base
{\pi }{n}}.} A concave bipyramid has a concave polygon base, and one example is a concave tetragonal bipyramid or an irregular concave octahedron. A bipyramid
Bipyramid
Shape with three sides
A triangle or trigon is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional
Triangle
Star polygon
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
Octagram
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
11-cell 57-cell Convex polygon Concave polygon Constructible polygon Cyclic polygon Equiangular polygon Equilateral polygon Regular polygon Penrose tile Polyform
List_of_mathematical_shapes
Method of triangulating polygons
properties: All convex polygons, but not all polygons, can be fan triangulated. Polygons with only one concave vertex can always be fan triangulated, as
Fan_triangulation
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
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
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)
Figure formed by two rays meeting at a common point
is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one interior
Angle
Time-telling device
special case of polar dials, in which the sharp edges of a prism of a concave polygon serve as the styles and the sides of the prism receive the shadow.
Sundial
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
Topics referred to by the same term
computer science Reentry (neural circuitry) in neuroscience Concave polygon, AKA reentrant polygon Reentry into the atmosphere of an orbiting body Re-entrant
Reentrant
Polygon clipping algorithm
merging. One or more concave polygons may produce more than one intersecting polygon. Convex polygons will only have one intersecting polygon. The same algorithm
Weiler–Atherton clipping algorithm
Weiler–Atherton_clipping_algorithm
Theorem on polygon dissections
are a few methods for this. For convex polygons one can cut off each vertex in turn, while for concave polygons this requires more care. A general approach
Wallace–Bolyai–Gerwien theorem
Wallace–Bolyai–Gerwien_theorem
Polygon with equally angled vertices
1, this represents a w-wound p/w/q/w star polygon, which is degenerate for the regular case. A concave indirect equiangular (pr+pl)-gon, with pr right
Equiangular_polygon
In geometry a line segment joining two nonconsecutive vertices of a polygon or polyhedron
convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon. Any n-sided polygon (n ≥
Diagonal
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
Shape bounded by non-intersecting line segments
angle is positive at a convex vertex or negative at a concave vertex. For every simple polygon, the sum of the external angles is 2 π {\displaystyle 2\pi
Simple_polygon
Mathematical problem in spectral theory
that have different shapes but identical eigenvalues. The regions are concave polygons. The proof that both regions have the same eigenvalues uses the symmetries
Hearing_the_shape_of_a_drum
Method in geometry for representing a polygon by a topological skeleton
that interpolates between two given polygonal chains. Tănase and Veltkamp propose to decompose concave polygons into unions of convex regions using straight
Straight_skeleton
Quadrilateral symmetric across a diagonal
intersecting circles. Kites as described here may be either convex or concave, although some sources restrict kite to mean only convex kites. A quadrilateral
Kite_(geometry)
Salt lake above the tide line, where evaporite deposits accumulate
Thermal contraction at night and expansion during the day leads to concave polygonal pans as the edges have been upturned, in part due to growth of evaporites
Sabkha
Polyhedron with 6 faces
hexahedra can only be realised as concave acoptic polyhedra. These are defined as the surfaces formed by non-crossing simple polygon faces, with each edge shared
Hexahedron
only in concave direction. All faces are made square to the bottom supporting surface to an accuracy of 2.5 \xm over the thickness of the polygon. The error
Precision_polygon
Shape with six sides
meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting)
Hexagon
Tiling of euclidean or hyperbolic space of three or more dimensions
Non-convex cells which pack without overlapping, analogous to tilings of concave polygons. These include a packing of the small stellated rhombic dodecahedron
Honeycomb_(geometry)
Representation method in chemistry
8-membered) are generally represented as regular polygons; larger ring sizes tend to be represented by concave polygons. Atoms in a group are ordered so that the
Skeletal_formula
Polygon with 16 edges
Hexadecagrams (16-sided star polygons) are included in the Girih patterns in the Alhambra. An octagonal star can be seen as a concave hexadecagon: The latter
Hexadecagon
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 18 edges
ring alternating the other two kinds of polygon. The regular octadecagon can tessellate the plane with concave hexagonal gaps. And another tiling mixes
Octadecagon
Polyhedron with 12 faces
to go past these limiting cases, creating concave or nonconvex pyritohedra. The endo-dodecahedron is concave and equilateral; it can tessellate space with
Dodecahedron
Common ideogram in modern culture
A five-pointed star (☆), geometrically an equilateral concave decagon, is a common ideogram in modern culture. Comparatively rare in classical heraldry
Five-pointed_star
Polyhedron with some pattern of nonconvexity
which self-intersect in a repetitive way. Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way
Star_polyhedron
Flat-sided three-dimensional shape
ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron"
Polyhedron
infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams. It is a special case of a right prism
Pentagrammic_prism
2D shape constructed by joining together identical basic polygons
joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle
Polyform
Theorem in geometry
quadrilateral form a parallelogram. If the quadrilateral is convex or concave (not complex), then the area of the parallelogram is half the area of the
Varignon's_theorem
Polygon with right angles and consecutive lengths
or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths. Golygons
Golygon
Geometric polygon
In Euclidean geometry, a spirolateral is a polygon created by a sequence of fixed vertex internal angles and sequential edge lengths 1,2,3,...,n which
Spirolateral
Mean position of all the points in a shape
at exactly the same place. This method can be extended (in theory) to concave shapes where the centroid may lie outside the shape, and virtually to solids
Centroid
Coinage of Cales, Italy
six-rayed star (Sambon 967) this is depicted by a pyramid built on a concave polygon (a dodecagon) with six points. The coins have the letter Γ (gamma)
Coinage_of_Cales
Polyhedron with parallel bases connected by triangles
composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented
Antiprism
Polyhedron with five faces
there are two distinct topological types. Notable polyhedra with regular polygon faces are: Square pyramid with four triangles and one square. Pyramids
Pentahedron
Element representing a value on a grid in three dimensional space
polygons are often explicitly represented by the coordinates of their vertices (as points). A direct consequence of this difference is that polygons can
Voxel
Geometric shape
entirely concave from below is y = y 0 + r 2 − ( x − x 0 ) 2 . {\displaystyle y=y_{0}+{\sqrt {r^{2}-(x-x_{0})^{2}}}.} If it is entirely concave from above
Semicircle
Flat rock surface subdivided by fractures
calcareous, sediments. They consist of polygonal cracking, often associated with individual 'plates' that tend to be concave upward, that characterizes the formation
Tessellated_pavement
Quadrilateral with two pairs of parallel sides
where a and b are the lengths of adjacent sides. Unlike any other convex polygon, a parallelogram cannot be inscribed in any triangle with less than twice
Parallelogram
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
Geometric relation between the roots of a polynomial and those of its derivative
within the convex hull of the roots of P, that is the smallest convex polygon containing the roots of P. When P has a single root then this convex hull
Gauss–Lucas_theorem
Sony's fourth home video game console
refinements. Among other tweaks, the caps of the analog sticks were given a concave design (similar to the Xbox 360 controller), the shape of the triggers
PlayStation_4
Polyhedron sliced by a plane into other polyhedra
Slobodan, Mišić; Obradović, Marija; Ðukanović, Gordana (2015). "Composite Concave Cupolae as Geometric and Architectural Forms" (PDF). Journal for Geometry
Composite_polyhedron
Triangle with circular arc edges
its perimeter. Other circular triangles can have a mixture of convex and concave circular arc edges. Three given angles θ 1 {\displaystyle \theta _{1}}
Circular_triangle
butterflies representing flames. The Olmecs of the Preclassic period fashioned concave mirrors that were capable of lighting fires. Mirrors were also associated
Mirrors in Mesoamerican culture
Mirrors_in_Mesoamerican_culture
Flight motion simulator at Disney parks
a mechanical lift system, a projected presentation on an 80 ft (24 m) concave 180-degree dome screen, and artificial scents and wind to simulate a hang
Soarin'
Combinatorial algorithm
195–208, doi:10.1007/BF01840359, MR 0895444. Wilber, Robert (1988), "The concave least-weight subsequence problem revisited", Journal of Algorithms, 9 (3):
SMAWK_algorithm
Shape with three inward-curved sides
angle of exactly π to be concave). Any polygon must have at least three convex angles because the total exterior angle of a polygon is 2π, the convex angles
Pseudotriangle
Extinct genus of dinosaurs
edge being slightly concave (more like Dreadnoughtus and Savannasaurus than the Saltasauridae, in which it was strongly concave). There was a ridge running
Patagotitan
Species of flowering plant
annulate; lower lip 3 fid, spreding, mid lobe large; upper lip 2 fid, erect, concave, villous outside, white. The corolla of Leucas aspera is 1 cm (0.39 in)
Leucas_aspera
dome-like vault having a square or polygonal base from which curved segments rise to a central point. Corbel vault – A concave formation of blocks, usually
List_of_architectural_vaults
1991 video game
made development of the game an easy task. The arcade cabinet featured a concave mirror to give off a sense of depth. The arcade version of Starblade received
Starblade
Optical instrument to view patterns due to repeated reflection
important by Brewster, was to place the reflecting panes in a draw tube with a concave lens to distinctly introduce surrounding objects into the reflected pattern
Kaleidoscope
Techniques for creating complex surfaces in 3D graphics software
while a degree 3 surface could (but does not necessarily) change once from concave to convex curvature. Some CAD systems use the term order instead of degree
Freeform_surface_modelling
Line of gamepads developed by Sony
with convex domed caps rather than the smooth plastic tips with recessed (concave) grooves found on the Dual Analog controller. Other visible differences
DualShock
Preorder on vectors of real numbers
_{j=1}^{d}|y_{j}-t|} . Each vector x {\displaystyle \mathbf {x} } can be plotted as a concave curve by connecting ( 0 , 0 ) , ( 1 , x 1 ↓ ) , ( 2 , x 1 ↓ + x 2 ↓ )
Majorization
points. Convex and Concave - a print by Escher in which many of the structure's features can be seen as both convex shapes and concave impressions. Convex
List_of_convexity_topics
Division of something into two equal or congruent parts
(broadly defined as a figure with three vertices connected by curves that are concave to the exterior of the deltoid, making the interior points a non-convex
Bisection
Optical illusion in which a white area takes on a pale tint
on a pale tint of a thin, bright, intensely colored polygon surrounding it if the coloured polygon is itself surrounded by a thin, darker border. The inner
Watercolor_illusion
roof hipped equally on all sides and centered over a square or regular polygonal floor plan. The sloping sides rise to a peak. For steep tower roof variants
List_of_roof_shapes
Invariance under a mathematical reflection
with reflection symmetry are kites, (concave) deltoids, rhombi, and isosceles trapezoids. All even-sided polygons have two simple reflective forms, one
Reflection_symmetry
Pyramid with a pentagon base
perpendicularly to the base's center. Like other right pyramids with a regular polygon as a base, this pyramid has pyramidal symmetry of cyclic group C 5 v {\displaystyle
Pentagonal_pyramid
Home video game consoles
grips, and has reduced and rounded trigger buttons. The D-pad is a new concave design that senior console designer Ryan Whitaker said was a means to merge
Xbox_Series_X_and_Series_S
Species of lichen
small polygons. A rim of dark tissue (prothallus) may surround the edges of the lichen. The fruiting body parts (apothecia) are flat to concave (especially
Aspicilia_phaea
of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams. It differs from the pentagrammic antiprism
Pentagrammic crossed-antiprism
Pentagrammic_crossed-antiprism
Multi-stage paper folding technique
central crease on each module outwards or convexly instead of inwards or concavely as for the icosahedron and other stellated polyhedra. The Mukhopadhyay
Modular_origami
Non-convex polyhedron with no triangulation
polyhedron consists of three tetrahedra, each lying between one of the concave dihedral edges of the Schönhardt polyhedron and one of the exterior diagonals
Schönhardt_polyhedron
Quadrilateral with sides of equal length
made up of colored polygons of four or five colors. The repeating patterns often used irregular four-, five- and six-sided polygons, but some contained
Lozenge_(shape)
2013 video game
revisit old curtains with new heads to complete it. The story occurs in a concave world representing Earth's Moon, inhabited by pseudo-folkloric characters:
Puppeteer_(video_game)
Any shape with straight sides can be cut from a single sheet of folded paper with one cut
making a single straight complete cut. Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the
Fold-and-cut_theorem
Curved structure that spans a space and may support a load
inextricably linked to the study of hanging chains, the corresponding curves or polygons are called funicular. Just like the shape of a hanging chain will vary
Arch
3d shape
of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams. It has 12 faces, 20 edges and 10 vertices
Pentagrammic_antiprism
Cupola with decagonal base
and one regular decagon. It has the property of convexity and regular polygonal faces, from which it is classified as the fifth Johnson solid. This cupola
Pentagonal_cupola
CONCAVE POLYGON
CONCAVE POLYGON
CONCAVE POLYGON
Surname or Lastname
English
English : variant spelling of Birks.
Girl/Female
Australian, Swedish
Chaste; Kind
Girl/Female
Arabic, Indian, Kannada, Muslim
Knowledge; Smart; Science; Metal
Girl/Female
Arabic, Muslim, Sindhi
Daughter of Safwan Bin Nawfal; Companion a
Girl/Female
American, Australian
God's Promise
Boy/Male
Irish
From the great river.
Girl/Female
Hindu, Indian
Royal; Kingly; The Great
Boy/Male
Tamil
Biblical
astonishment; fear
Boy/Male
British, English
Powerful Traveler
CONCAVE POLYGON
CONCAVE POLYGON
CONCAVE POLYGON
CONCAVE POLYGON
CONCAVE POLYGON
a.
Arched; concave.
p. pr. & vb. n.
of Concave
a.
Congenitally united; growing from one base, or united at their bases; united into one body; as, connate leaves or athers. See Illust. of Connate-perfoliate.
a.
Concave on both sides; as, biconcave vertebrae.
a.
Plane or flat on one side, and concave on the other; as, a plano-concave lens. See Lens.
v. t.
To yield or suffer; to surrender; to grant; as, to concede the point in question.
n.
Also used adjectively; as, the conacre system or principle.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
a.
Hollow and curved or rounded; vaulted; -- said of the interior of a curved surface or line, as of the curve of the of the inner surface of an eggshell, in opposition to convex; as, a concave mirror; the concave arch of the sky.
a.
Convex on one side, and concave on the other. The curves of the convex and concave sides may be alike or may be different. See Meniscus.
n.
A concave molding.
v. t.
To form in the mind; to plan; to devise; to generate; to originate; as, to conceive a purpose, plan, hope.
v. t.
To make hollow or concave.
a.
Having both ends concave; biconcave; -- said of vertebrae.
n.
The body of cardinals shut up in the conclave for the election of a pope; hence, the body of cardinals.
imp. & p. p.
of Concave
a.
Specifically, having such a combination of concave and convex sides as makes the focal axis the shortest line between them. See Illust. under Lens.
a.
Slightly concave.
a.
Concave.
a.
Concave or hollow on both sides; double concave.