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52 Polytope topics matching:
Filter this Collection| x name | x image | x Number of Dimensions | x article |
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| x Uniform polyexon |
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In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets.
A uniform 7-polytope is one which is vertex-transitive, and constructed from uniform 6...
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| x Catalan solid |
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In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865.
The Catalan solids are all convex. They...
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| x Convex polytope |
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space R. Some authors use the terms "convex polytope" and "convex polyhedron" interchangeably, while others...
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| x Regular polytope |
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In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and...
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| x Semiregular polyhedron |
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The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.
In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly...
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| x Uniform polytope |
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A uniform polytope is a vertex-transitive polytope made from uniform polytope facets of a lower dimension. Uniform polytopes of 2 dimensions are the regular polygons.
This is a generalization of the older category of semiregular polytopes, but also...
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| x Abstract polytope |
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In mathematics, an abstract polytope, informally speaking, is a structure which considers only the combinatorial properties of a traditional polytope, ignoring many of its other properties, such as angles, edge lengths, etc. No space, such as...
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| x Apeirogon |
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An apeirogon is a degenerate polygon with a countably infinite number of sides.
Like any polygon, it is a sequence of line segments (edges) and angles (corners). But whereas an ordinary polygon has no ends because it is a closed circuit, an...
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| x Decagon |
In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and each internal angle equal to 144°. Its Schläfli symbol is {10}.
The area of a regular decagon is: ...
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| x Decagram |
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In geometry, a decagram is a 10-sided star polygon. There is one regular decagram star polygon, {10/3}, containing the vertices of a regular decagon, but connected by every third point.
There are two regular decagram star figures: {10/2} and {10/4},...
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| x Digon |
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In geometry, a digon or 2-gon is a polygon with two sides (edges) and two vertices. It is degenerate in a Euclidean space, but may be non-degenerate in a spherical space.
A digon must be regular because its two edges are the same length. It has...
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| x Dodecagon |
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In geometry, a dodecagon is any polygon with twelve sides and twelve angles.
It usually refers to a regular dodecagon, having all sides of equal length and all angles equal to 150°. Its Schläfli symbol is {12}.
The area of a regular dodecagon with...
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| x Enneadecagon |
In geometry, an enneadecagon is a polygon with 19 sides and angles. It is also known as an enneakaidecagon or a nonadecagon.
The radius of the circumcircle of the regular enneadecagon with side length t is
The area of a regular enneadecagon, where t...
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| x Enneagram |
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In geometry, an enneagram is a nine-pointed geometric figure. It is sometimes called a nonagram.
A regular enneagram (a nine-sided star polygon) is constructed using the same points as the regular enneagon but connected in fixed steps. It has two...
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| x Equiangular polygon |
In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal then it is a regular polygon.
The only equiangular triangle is the equilateral triangle. Rectangles, including the...
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| x Equilateral pentagon |
In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique,...
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| x Five-pointed star |
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A five-pointed star (☆) is a very common ideogram throughout the world. If the colinear edges are joined together a pentagram is produced, which is the simplest of the unicursal star polygons, and a symbol of mystical and magical significance.
The...
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| x Henagon |
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In geometry a henagon (or monogon) is a polygon with one edge and one vertex. It has Schläfli symbol {1}. Since a henagon has only one side and only one interior angle, every henagon is regular by definition.
In Euclidean geometry a henagon is...
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| x Hendecagon |
In geometry, a hendecagon (also undecagon) is an 11-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and gon– "corner", is often preferred to the hybrid undecagon, whose first syllable un– is Latin for "one".)
A regular hendecagon...
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| x Hendecagram |
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A hendecagram is a star polygon that has eleven vertices. There are 4 regular forms: {11/2}, {11/3}, {11/4}, {11/5}.
The regular hendecagon and hendecagrams combine together to represent a complete graph with 11 vertices. This is also the graph of...
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| x Heptadecagon |
In geometry, a heptadecagon (or 17-gon) is a seventeen-sided polygon.
The regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge), as was shown by Carl Friedrich Gauss in 1796...
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| x Heptagon |
In geometry, a heptagon is a polygon with seven sides and seven angles. In a regular heptagon, in which all sides and all angles are equal, the sides meet at an angle of 5π/7 radians, 128.5714286 degrees. Its Schläfli symbol is {7}. The area (A) of...
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| x Heptagram |
A heptagram or septegram is a seven-pointed star drawn with seven straight strokes.
In general, a heptagram is any self-intersecting heptagon (7-sided polygon).
There are two regular heptagrams, labeled as {7/2} and {7/3}, with the second number...
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| x Hexadecagon |
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In mathematics, a hexadecagon (sometimes called a hexakaidecagon) is a polygon with 16 sides and 16 vertices.
A regular hexadecagon is constructible with a compass and straightedge.
Each angle of a regular hexadecagon is 157.5 degrees, and the total...
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| x Hexagon |
In geometry, a hexagon (from Greek ἕξ hex, "six") is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol {6}. The total of the internal angles of any hexagon is 720°.
A regular hexagon has all sides of the same length,...
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| x Hexagram |
A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure, {6|2}, 2{3}, or {{3}}, the compound of two equilateral triangles. The intersection is a regular hexagon.
It is used in historical, religious and cultural contexts, for...
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| x Icosagon |
In geometry, an icosagon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees.
One interior angle in a regular icosagon is 162°, meaning that one exterior angle would be 18°.
The regular icosagon is a constructible...
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| x Isothetic polygon |
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An isothetic polygon is a polygon whose alternate sides belong to two parametric families of straight lines which are pencils of lines with centers at two points (possibly in the infinity). The most well-known example of isothetic polygons are...
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| x Lemoine hexagon |
The Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. The circumcircle of the Lemoine hexagon is the...
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| x Nonagon |
In geometry, a nonagon /ˈnɒnəɡɒn/ (or enneagon /ˈɛniːəɡɒn/) is a nine-sided polygon.
The name "nonagon" is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone...
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| x Octadecagon |
An octadecagon is a polygon with 18 sides and 18 vertices. Another name for an octadecagon is octakaidecagon.
A regular octadecagon cannot be constructed using a compass and straightedge.
A regular triangle, enneagon, and octadecagon can completely...
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| x Octagon |
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is a polygon that has eight sides. A regular octagon is represented by the Schläfli symbol {8}.
A regular octagon is a closed figure with sides of the same length and...
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| x Octagram |
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In geometry, an octagram is an eight-sided star polygon.
In 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 8-sided star, connected by every 3rd...
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| x Parallelogon |
A parallelogon is a convex polygon such that images of the polygon under translations only tile the plane when fitted together along entire sides.
A parallelogon must have an even number of sides and opposite sides must be equal in length and...
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| x Pentadecagon |
In geometry, a pentadecagon (or pentakaidecagon) is any 15-sided, 15-angled, polygon.
A regular pentadecagon has interior angles of 156°, and with a side length a, has an area given by
A regular triangle, decagon, and pentadecagon can completely...
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| x Pentagon |
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In geometry, a pentagon (from pente, which is Greek for the number 5) is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self...
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| x Pentagram |
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A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes. The word pentagram comes from the Greek word πεντάγραμμον (pentagrammon), a noun form of πεντάγραμμος ...
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| x Right triangle |
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A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for...
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| x Tetradecagon |
In geometry, a tetradecagon (or tetrakaidecagon) is a polygon with 14 sides and angles.
The area of a regular tetradecagon of side length a is given by
The regular tetradecagon is used as the shape of some commemorative gold and silver Malaysian...
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| x Triangle |
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.
In Euclidean geometry any three non-collinear points...
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| x Triskaidecagon |
In geometry, a tridecagon (or triskaidecagon) is a polygon with 13 sides and angles.
The measure of each internal angle of a regular tridecagon is approximately 152.308 degrees, and the area with side length a is given by
The regular tridecagon is...
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| x Unicursal Hexagram |
The unicursal hexagram is a hexagram or six-pointed star that can be traced or drawn unicursally, in one continuous line rather than by two overlaid triangles. The hexagram can also be depicted inside a circle with the points touching it.
English...
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| x Polygon |
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In geometry a polygon ( /ˈpɒlɪɡɒn/) is a flat shape consisting of straight lines that are joined to form a closed chain or circuit.
A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight...
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| x Dodecahedron |
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In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα, dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces, but usually a regular dodecahedron is meant: a Platonic solid. It is composed of 12 regular...
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| x Elongated pentagonal cupola |
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In geometry, the elongated pentagonal cupola is one of the Johnson solids (J20). As the name suggests, it can be constructed by elongating a pentagonal cupola (J5) by attaching a decagonal prism to its base. The solid can also be seen as an...
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| x Square antiprism | 3 |
In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube.
If all its faces are regular, it is a semiregular...
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| x Polyhedron |
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In elementary geometry a polyhedron (plural polyhedra or polyhedrons) is a geometric solid in three dimensions with flat faces and straight edges. The word polyhedron comes from the Classical Greek πολύεδρον, as poly- (stem of πολύς, "many") + ...
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| x Tesseract |
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In geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces...
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| x Polychoron | 4 |
In geometry, a polychoron or 4-polytope is a four-dimensional polytope. It is a connected and closed figure, composed of lower dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly...
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| x Hypercube |
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions,...
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| x Square |
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In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles (90-degree angles, or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with...
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| x Cube |
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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of...
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