If a simple polygon is not convex, it is called concave. At least one internal angle of a concave polygon is larger than 180 degrees. A concave polygon is often called re-entrant polygon (but in some cases the latter term has a different meaning). ...

See also:

Convex polygon, Convex polygon - Concave polygons

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See also:

Polygon, Polygon - Names and types, Polygon - Naming polygons, Polygon - Taxonomic classification, Polygon - Properties, Polygon - Angles, Polygon - Area, Polygon - Construction, Polygon - Point in polygon test, Polygon - Special cases

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An orientable closed surface of genus n has the following standard fundamental polygon: A non-orientable closed surface of (non-orientable) genus n has the following standard fundamental polygon: ...

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Fundamental polygon, Fundamental polygon - Examples, Fundamental polygon - Standard fundamental polygons, Fundamental polygon - Fundamental polygon of a compact Riemann surface, Fundamental polygon - Metric fundamental polygon, Fundamental polygon - Standard fundamental polygon, Fundamental polygon - Example, Fundamental polygon - Area

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As applied to a polygon, a diagonal is a line segment joining two vertices that are not adjacent. Therefore a quadrilateral has two diagonals, joining opposite pairs of vertices. For a convex polygon the diagonals run inside the polygon. This is not so for re-entrant polygons. In fact a polygon is convex if and only if the diagonals are internal. When n is the number of vertices in a polygon and d is the number of possible different diagonals, each vertex has possible diagonals to all other vertices save for itsel ...

See also:

Diagonal, Diagonal - Polygons, Diagonal - Matrices, Diagonal - Geometry

Read more here: » Diagonal: Encyclopedia II - Diagonal - Polygons

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. Constructible polygon - Conditions for constructibility. Some regular polygons are easy to construct with compass and straightedge; others are not. This led to the question being posed: is it possible to construct all regular n-gons with compass and straightedge? If not ...

Including:

• Constructible polygon - Conditions for constructibility
• Constructible polygon - General theory
• Constructible polygon - Detailed results in terms of Fermat primes
• Constructible polygon - Compass-and-straightedge constructions
• Constructible polygon - Other constructions

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In geometry, the circumcircle of a given two-dimensional geometric shape is a circle which contains the shape completely within it. For a triangle, it is the unique circle containing all three vertices. The center of this circumcircle is known as the shape's circumcenter. Note that although the circumcircle of an acute triangle is indeed the smallest circle containing this triangle, this is not true of obtuse triangles. Circumcircle - Cyclic polygons. At least three ver ...

Including:

• Circumcircle - Cyclic polygons
• Circumcircle - Circumcircles of triangles
• Circumcircle - Circumcircle equation
• Circumcircle - Circumcircle of circles

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In mathematics (topology), a surface is a two-dimensional manifold. Examples arise in three-dimensional space as the boundaries of three-dimensional solid objects. The surface of a fluid object, such as a rain drop or soap bubble, is an idealisation. To speak of the surface of a snowflake, which has a great deal of fine structure, is to go beyond the simple mathematical definition. For the nature of real surfaces see surface tension, ...

Including:

• Surface - Examples
• Surface - Definition
• Surface - Classification of closed surfaces
• Surface - Compact surfaces
• Surface - Embeddings in R3
• Surface - Differential geometry
• Surface - Some models
• Surface - Fundamental polygon
• Surface - Connected sum of surfaces
• Surface - Algebraic surface

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3D Studio Max (sometimes called 3ds Max or just MAX) is a 3D computer graphics and animation program, written by Autodesk Media & Entertainment (formerly known as Discreet and Kinetix). It was developed as a successor to 3D Studio for DOS, but for the Win32 platform. Kinetix was later merged with Autodesk's latest acquisition, Discreet Logic. The current version of 3DS Max as of September 2005 is 8. 3D Studio Max - Overview. 3ds Max is one of the most widely-used 3D an ...

Including:

• 3D Studio Max - Overview
• 3D Studio Max - Modeling Methods
• 3D Studio Max - Modeling with primitives
• 3D Studio Max - NURMS
• 3D Studio Max - Surface tool
• 3D Studio Max - NURBS
• 3D Studio Max - Polygon modelling
• 3D Studio Max - Particle systems
• 3D Studio Max - Features
• 3D Studio Max - MAXScript
• 3D Studio Max - Character Studio
• 3D Studio Max - Mental Ray

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A zonohedron is a convex polyhedron where every face is a polygon with point symmetry or, equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic solids, only the cube 4.4.4 is a zonohedron Of the Archimedean solids, only the truncated octahedron 4.6.6, th ...

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A chiliagon (pronounced /ˈkɪli.əˌgɑn/) is a polygon with 1000 sides. The measure of each angle in a regular chiliagon is 179.64°. See also: Chiliagonal number ...

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In mathematics, there are several notions of constructibility: a point in the Euclidean plane that can be constructed with unruled straightedge and compass. Also, any complex number associated to such a point; see constructible number. a regular polygon that can be constructed with unruled straightedge and compass; see constructible polygon. a theorem that can be proved by constructivist logic; see mathematical constructivism. a set in Kurt Gödel's universe L, which may be constructed by

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The word concave means curving in or hollowed inward. The term may rever to Concave lens — a lens with inward-curving (concave) surfaces. Concave polygon — a polygon which is not convex. Concave function — a type a function which is very related to convex functions. In addition, the term concave upwards is used for convex functions, and concave downwards for concave functions. Other related archivesConcave function

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In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. They are distinct from the Platonic solids, which are composed of only one type of polygon meeting in identical vertices, and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices. Archimedean solid - Origin of name. The Archimedean solids take their name from Archimedes, who discussed them ...

Including:

• Archimedean solid - Origin of name
• Archimedean solid - Classification

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A heptagram or septagram is a seven-pointed star drawn with seven straight strokes. There are two kinds of heptagram: Acute heptagram, the {7/3} star polygon. Obtuse heptagram, the {7/2} star polygon. The acute heptagram is known as the Elven Star or Fairy Star, a sacred symbol to Wiccans who follow the Faery tradition. Similarly, it has been adopted as an identifier by members of the Otherkin subculture. Blue Star Wicca also uses the symbol, where it is referred to simply as a septagram. The acute heptagram is also a sy ...

Including:

• Heptagram - 3D

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Wings 3D is a free and open source polygon mesh modeler inspired by Nendo and Mirai from Izware. Wings 3D is available for most platforms, including Windows, Linux and Mac OS X, using the Erlang environment. Wings 3D is best suited for modeling and texturing low-polygon meshes, towards which its interface is geared. When compared to other open-source modelling programs such as Blender, its GUI is minimalistic. This allows a very flexible way of working, but it also means that Wings 3D is more limited than other modelling ...

Including:

• Wings 3D - InterWiki links

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A cell is a three-dimensional object that is part of a higher-dimensional object, such as a polychoron. A cell is related to higher-dimensional objects in the way that a face, or two-dimensional polygon, is related to 3-dimensional objects. For example, a cell is to a 4-dimensional polytope, or polychoron, what a face is to a 3-dimensional polytope, or polyhedron. See also. cell complex ...

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A containment hierarchy is a hierarchical collection of strictly nested sets. Each entry in the hierarchy designates a set such that the previous entry is a strict superset, and the next entry is a strict subset. For example, all rectangles are quadrilaterals, but not all quadrilaterals are rectangles, and all squares are rectangles, but not all rectangles are squares. A taxonomy is a classic example of a containment hierarchy: In geometry: shape, polygon, quadrilateral, rectangle, square In biology: anima ...

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The taxonomic classification of polygons is illustrated by the following tree: Polygon / \ Simple Complex / \ Convex Concave / Cyclic / Regular A polygon is called simple if it is described by a single, non-intersecting boundary (he ...

See also:

Polygon, Polygon - Names and types, Polygon - Naming polygons, Polygon - Taxonomic classification, Polygon - Properties, Polygon - Angles, Polygon - Area, Polygon - Construction, Polygon - Point in polygon test, Polygon - Special cases

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We will assume Euclidean geometry throughout. An n-gon has 2n degrees of freedom, including 2 for position and 1 for rotational orientation, and 1 for over-all size, so 2n-4 for shape. In the case of a line of symmetry the latter reduces to n-2. Let k≥2. For an nk-gon with k-fold rotational symmetry (Ck), there are 2n-2 degrees of freedom for the shape. With additional mirror-image symmetry (Dk) there are n-1 degrees of freedom. < ...

See also:

Polygon, Polygon - Names and types, Polygon - Naming polygons, Polygon - Taxonomic classification, Polygon - Properties, Polygon - Angles, Polygon - Area, Polygon - Construction, Polygon - Point in polygon test, Polygon - Special cases

Read more here: » Polygon: Encyclopedia II - Polygon - Properties

Some special cases are: Angle of 0° or 180° (degenerate case) Two non-adjacent sides are on the same line Equilateral polygon: a polygon whose sides are equal (Williams 1979, pp. 31-32) Equiangular polygon: a polygon whose vertex angles are equal (Williams 1979, p. 32) A triangle is equilateral iff it is equiangular. An equilateral quadrilateral is a rhombus, an equiangular quadrilateral is a rectangle or an "ang ...

See also:

Polygon, Polygon - Names and types, Polygon - Naming polygons, Polygon - Taxonomic classification, Polygon - Properties, Polygon - Angles, Polygon - Area, Polygon - Construction, Polygon - Point in polygon test, Polygon - Special cases

Read more here: » Polygon: Encyclopedia II - Polygon - Special cases