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B4 Polytope
In 4-dimensional geometry, there are 15 uniform 4-polytopes with B4 symmetry. There are two regular forms, the tesseract and 16-cell, with 16 and 8 vertices respectively. Visualizations They can be visualized as symmetric orthographic projections in Coxeter planes of the B5 Coxeter group, and other subgroups. Symmetric orthographic projections of these 32 polytopes can be made in the B5, B4, B3, B2, A3, Coxeter planes. Ak has '' +1' symmetry, and Bk has '' k' symmetry. These 32 polytopes are each shown in these 5 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position. The pictures are drawn as Schlegel diagram perspective projections, centered on the cell at pos. 3, with a consistent orientation, and the 16 cells at position 0 are shown solid, alternately colored. Coordinates The tesseractic family of 4-polytopes are given by the convex hulls of the base points listed in the following ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthographic Projection
Orthographic projection (also orthogonal projection and analemma) is a means of representing Three-dimensional space, three-dimensional objects in Two-dimensional space, two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are ''not'' orthogonal to the projection plane. The term ''orthographic'' sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the ''primary views''. If the principal planes or axes of an object in an orthographic projection are ''not'' parallel with the projection plane, the depiction is called ''axonometric'' or an ''auxiliary views''. (''A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-cube T1
In geometry, a tesseract is the four-dimensional analogue 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 six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book ''A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spelled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-cube T01 B3
In geometry, a tesseract is the four-dimensional analogue 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 six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book ''A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spelled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-cube T01
In geometry, a tesseract is the four-dimensional analogue 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 six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book '' A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Tesseract
In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract. There are three truncations, including a bitruncation, and a tritruncation, which creates the ''truncated 16-cell''. Truncated tesseract The truncated tesseract is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra. Alternate names * Truncated tesseract (Norman W. Johnson) * Truncated tesseract (Acronym tat) (George Olshevsky, and Jonathan Bowers) Construction The truncated tesseract may be constructed by truncating the vertices of the tesseract at 1/(\sqrt+2) of the edge length. A regular tetrahedron is formed at each truncated vertex. The Cartesian coordinates of the vertices of a truncated tesseract having edge length 2 is given by all permutations of: :\left(\pm1,\ \pm(1+\sqrt),\ \pm(1+\sqrt),\ \pm(1+\sqrt)\right) Projections In the truncated cube first parallel projection of the truncated tesseract into 3-dimensional space, the image is laid out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
16-cell Net
In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid .Matila Ghyka, ''The Geometry of Art and Life'' (1977), p.68 It is a part of an infinite family of polytopes, called cross-polytopes or ''orthoplexes'', and is analogous to the octahedron in three dimensions. It is Coxeter's \beta_4 polytope. Conway's name for a cross-polytope is orthoplex, for ''orthant complex''. The dual polytope is the tesseract (4-cube), which it can be combined with to form a compound figure. The 16-cell has 16 cells as the tesseract has 16 vertices. Geometry The 16-cell is the second in the sequence of 6 convex regular 4-polytopes (in order of size and complexity). Each of its 4 successor convex regular 4-polytopes can be constructed as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schlegel Wireframe 16-cell
Schlegel is a German occupational surname. Notable people with the surname include: * Anthony Schlegel (born 1981), former American football linebacker * August Wilhelm Schlegel (1767–1845), German poet, older brother of Friedrich * Brad Schlegel (born 1968), Canadian ice hockey player * Bernhard Schlegel (born 1951), German-Canadian chemist and professor at Wayne State University * Carmela Schlegel (born 1983), retired Swiss swimmer * Catharina von Schlegel (1697 – after 1768), German hymn writer * Dorothea von Schlegel (1764–1839), German novelist and translator, wife of Friedrich Schlegel * Elfi Schlegel (born 1964), former Canadian gymnast and sportscaster for NBC Sports * Frits Schlegel (1896–1965), Danish architect * Gustaaf Schlegel (1840–1903), Dutch sinologist and field naturalist * Hans Schlegel (born 1951), German astronaut * Helmut Schlegel (born 1943), German Franciscan, priest, author, meditation instructor, songwriter * Hermann Schlegel (1804–1884), Germa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-cube T3 A3
In geometry, a tesseract is the four-dimensional analogue 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 six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book ''A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spelled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-cube T3 B2
In geometry, a tesseract is the four-dimensional analogue 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 six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book ''A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spelled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-demicube T0 D4
In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid .Matila Ghyka, ''The Geometry of Art and Life'' (1977), p.68 It is a part of an infinite family of polytopes, called cross-polytopes or ''orthoplexes'', and is analogous to the octahedron in three dimensions. It is Coxeter's \beta_4 polytope. Conway's name for a cross-polytope is orthoplex, for ''orthant complex''. The dual polytope is the tesseract (4-cube), which it can be combined with to form a compound figure. The 16-cell has 16 cells as the tesseract has 16 vertices. Geometry The 16-cell is the second in the sequence of 6 convex regular 4-polytopes (in order of size and complexity). Each of its 4 successor convex regular 4-polytopes can be constructed as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectified Tesseract Net
Rectification has the following technical meanings: Mathematics * Rectification (geometry), truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points * Rectifiable curve, in mathematics * Rectifiable set, in mathematics Science * GHK flux equation#Rectification, in biology, a process in cell membranes Technology * Image rectification, adjustment of images to simplify stereo vision or to map images to a map coordinate system (GIS) * The function of a rectifier, a device that converts alternating electrical current to direct current * Rectified airspeed, a means of displaying the airspeed of high-speed aircraft * Rectification (chemical/process engineering), countercurrent distillation, a unit operation also used for the production of rectified spirit (see Distillation#Fractional distillation) Other uses * Rectification (law), an equitable legal remedy whereby a court orders a change in a written document to reflect what ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schlegel Half-solid Rectified 8-cell
Schlegel is a German occupational surname. Notable people with the surname include: * Anthony Schlegel (born 1981), former American football linebacker * August Wilhelm Schlegel (1767–1845), German poet, older brother of Friedrich * Brad Schlegel (born 1968), Canadian ice hockey player * Bernhard Schlegel (born 1951), German-Canadian chemist and professor at Wayne State University * Carmela Schlegel (born 1983), retired Swiss swimmer * Catharina von Schlegel (1697 – after 1768), German hymn writer * Dorothea von Schlegel (1764–1839), German novelist and translator, wife of Friedrich Schlegel * Elfi Schlegel (born 1964), former Canadian gymnast and sportscaster for NBC Sports * Frits Schlegel (1896–1965), Danish architect * Gustaaf Schlegel (1840–1903), Dutch sinologist and field naturalist * Hans Schlegel (born 1951), German astronaut * Helmut Schlegel (born 1943), German Franciscan, priest, author, meditation instructor, songwriter * Hermann Schlegel (1804–1884), Ger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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