54 relations: Algebraic expression, Apothem, Area, Bisection, Centered decagonal number, Chaim Goodman-Strauss, Circle, Circumscribed circle, Compass-and-straightedge construction, Constructible polygon, Coxeter element, Cyclic group, Decagonal number, Decagram (geometry), Diameter, Dihedral group, Directed graph, Dodecahedron, Dual polygon, Fermat number, Figurate number, Geometry, Golden ratio, Harold Scott MacDonald Coxeter, Icosahedral symmetry, Icosahedron, Icosidodecahedron, Inscribed figure, Isogonal figure, Isotoxal figure, John Horton Conway, Multiplicative inverse, Pentagon, Pentagonal antiprism, Pentagrammic antiprism, Pentagrammic crossed-antiprism, Petrie polygon, Polygon, Power of two, Projection (linear algebra), Ratio, Regular polygon, Rhombic triacontahedron, Schläfli symbol, Skew polygon, Star polygon, Trigonometry, Truncation (geometry), Zonogon, 10-cube, ..., 5-cube, 5-orthoplex, 6-demicube, 9-simplex. Expand index (4 more) » « Shrink index
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
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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.
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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
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In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
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A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers.
Chaim Goodman-Strauss (born June 1967 in Austin TX) is an American mathematician who works in convex geometry, especially aperiodic tiling.
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A circle is a simple closed shape.
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In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.
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In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
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In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
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A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon).
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In geometry, a decagram is a 10-point star polygon.
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In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
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In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
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In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.
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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.
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In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.
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In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.
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The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers).
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Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
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Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.
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In geometry, an icosahedron is a polyhedron with 20 faces.
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In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.
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An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.
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In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
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In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.
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John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.
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In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
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In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
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In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.
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In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
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In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.
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In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.
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In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
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In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces.
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In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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In geometry, a skew polygon is a polygon whose vertices are not all coplanar.
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In geometry, a star polygon is a type of non-convex polygon.
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Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
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In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
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In geometry, a zonogon is a centrally symmetric convex polygon.
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In geometry, a 10-cube is a ten-dimensional hypercube.
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In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.
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In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.
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In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.
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In geometry, a 9-simplex is a self-dual regular 9-polytope.
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