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The Big Bang Theory Series 8 Episode 2 - The Junior Professor Solution: features this solid as the answer to an impromptu science quiz the main four characters have in Leonard and Sheldon's apartment, and is also illustrated in Chuck Lorre's Vanity Card #461 at the end of that episode.
Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
3. Restriction of a function: if f is a function, and S is a subset of its domain, then | is the function with S as a domain that equals f on S. 4. Conditional probability: () denotes the probability of X given that the event E occurs. Also denoted (/); see "/". 5.
The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices ...
3.8.8: 8 triangles 6 octagons: 36 24 O h: Truncated octahedron: 4.6.6: 6 squares 8 hexagons 36 24 O h: Rhombicuboctahedron: 3.4.4.4: 8 triangles 18 squares 48 24 O h: Truncated cuboctahedron: 4.6.8: 12 squares 8 hexagons 6 octagons 72 48 O h: Snub cube: 3.3.3.3.4: 32 triangles 6 squares 60 24 O Icosidodecahedron: 3.5.3.5: 20 triangles 12 ...
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
The tesseract is one of 6 convex regular 4-polytopes. In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope.They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions.