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Compound of twelve pentagonal antiprisms with rotational freedom; Compound of twelve pentagonal prisms; Compound of twelve pentagrammic prisms; Compound of twelve tetrahedra with rotational freedom; Compound of twenty octahedra; Compound of twenty octahedra with rotational freedom; Compound of twenty tetrahemihexahedra; Compound of twenty ...
Regular polygrams {n/d}, with red lines showing constant d, and blue lines showing compound sequences k{n/d} In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also include disconnected sets of edges, called a compound polygon.
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. This is a listing of articles which explain some of these functions in more detail.
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
The compound of five tetrahedra is a geometric illustration of the notion of orbits and stabilizers, as follows.. The symmetry group of the compound is the (rotational) icosahedral group I of order 60, while the stabilizer of a single chosen tetrahedron is the (rotational) tetrahedral group T of order 12, and the orbit space I/T (of order 60/12 = 5) is naturally identified with the 5 ...
In mathematics, the exterior algebra or Grassmann algebra of a vector space is an associative algebra that contains , which has a product, called exterior product or wedge product and denoted with , such that = for every vector in .
For example, when transforming the 7-square to the 8-square, we add 15 elements; these adjunctions are the 8s in the above figure. This gnomonic technique also provides a proof that the sum of the first n odd numbers is n 2; the figure illustrates 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8 2. First five terms of Nichomachus's theorem