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geometry, a truncated 6-simplex is a convex uniform 6-polytope, being a truncation of the regular 6-simplex. There are unique 3 degrees of truncation. Vertices
Truncated_6-simplexes
geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees of truncation. Vertices
Truncated_8-simplexes
Uniform 6-polytope
constructed from 14 snub 5-simplexes, 42 snub 5-cell antiprisms, 70 3-s{3,4} duoantiprisms, and 2520 irregular 5-simplexes filling the gaps at the deleted
Pentellated_6-simplexes
facets of the bicantitruncated 7-orthoplex. The cantellated 6-simplexes are in a set of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown
Cantellated_6-simplexes
Uniform 7-polytope
geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex. There are unique 3 degrees of truncation. Vertices
Truncated_7-simplexes
4-faces (6 5-cell and 6 truncated 5-cells). Truncated hexateron (Acronym: tix) (Jonathan Bowers) The vertices of the truncated 5-simplex can be most simply
Truncated_5-simplexes
Uniform 8-polytope
cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube. Truncated demiocteract Truncated hemiocteract; Acronym:
Cantic_8-cube
analogue would be a truncated tetrahedron (truncated 3-demicube), and Coxeter diagram or as a cantic cube. Truncated demihepteract Truncated hemihepteract (acronym:
Cantic_7-cube
symmetrically-ringed Coxeter-Dynkin diagram. The runcinated 6-simplexes are in a set of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown
Runcinated_6-simplexes
the steriruncicantitruncated 7-orthoplex. The stericated 6-simplexes are in a set of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown
Stericated_6-simplexes
Uniform 6-polytope
Its vertex figure is a rectified 5-cell pyramid. Truncated icosihepta-heptacontadi-peton as a truncated 27-72 facetted polypeton (Acronym: tojak) Vertices
2_21_polytope
pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of
5-simplex_honeycomb
64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the
Stericated_6-orthoplexes
Type of 7-polytope
6th-order truncations (hexication) from the regular 7-simplex. There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations
Hexicated_7-simplexes
4th order truncations (sterication) of the regular 7-simplex. There are 14 unique sterication for the 7-simplex with permutations of truncations, cantellations
Stericated_7-simplexes
Regular 5-polytope
Dih6 or simple rotation group [6,2]+, order 12. The compound of two 5-simplexes in dual configurations can be seen in this A6 Coxeter plane projection
5-simplex
Uniform polychoron
series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified
Rectified_5-cell
Cube. The birectified 5-simplex is the intersection of two regular 5-simplexes in dual configuration. The vertices of a birectification exist at the
Rectified_5-simplexes
Convex uniform 7-polytope in seven-dimensional geometry
8-orthoplex. The trirectified 7-simplex is the intersection of two regular 7-simplexes in dual configuration. E. L. Elte identified it in 1912 as a semiregular
Rectified_7-simplexes
order truncations (runcination) of the regular 8-simplex. There are eleven unique runcinations of the 8-simplex, including permutations of truncation and
Runcinated_8-simplexes
There are unique 4 degrees of cantellation for the 5-simplex, including truncations. The cantellated 5-simplex has 60 vertices, 240 edges, 290 faces (200
Cantellated_5-simplexes
Four-dimensional analogue of the tetrahedron
face-to-face) with the two opposite vertices centered. In the case of simplexes such as the 5-cell, certain irregular forms are in some sense more fundamental
5-cell
3rd order truncations (runcination) of the regular 7-simplex. There are 8 unique runcinations of the 7-simplex with permutations of truncations, and cantellations
Runcinated_7-simplexes
hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex. Acronym: supane (Jonathan Bowers) The Cartesian
Hexicated_8-simplexes
(360 truncated octahedra, 90 cubes, and 90 hexagonal prisms), and 62 4-faces (12 omnitruncated 5-cells, 30 truncated octahedral prisms, and 20 6-6 duoprisms)
Stericated_5-simplexes
truncations (heptellation) from the regular 8-simplex. There are 35 unique heptellations for the 8-simplex, including all permutations of truncations
Heptellated_8-simplexes
There are two degrees of truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10
Truncated_5-cell
Class of eight-dimensional polytopes
order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation
Stericated_8-simplexes
six unique cantellations for the 8-simplex, including permutations of truncation. Small rhombated enneazetton (acronym: srene) (Jonathan Bowers) The Cartesian
Cantellated_8-simplexes
Simplex formed from a right-angled path
orthoschemes. Coxeter identifies various orthoschemes as the characteristic simplexes of the polytopes they generate by reflections. The characteristic simplex
Schläfli_orthoscheme
3rd order truncations (Runcination) of the regular 5-simplex. There are 4 unique runcinations of the 5-simplex with permutations of truncations, and cantellations
Runcinated_5-simplexes
8-polytope with 5th order truncations of the regular 8-simplex. There are two unique pentellations of the 8-simplex. Including truncations, cantellations, runcinations
Pentellated_8-simplexes
Topological invariant in mathematics
\chi =k_{0}-k_{1}+k_{2}-k_{3}+\cdots ,} where kn denotes the number of n-simplexes in the complex. More generally still, for any topological space, we can
Euler_characteristic
of the regular 7-simplex. There are unique 6 degrees of cantellation for the 7-simplex, including truncations. Small rhombated octaexon (acronym: saro)
Cantellated_7-simplexes
Seven-dimensional geometric object
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
Uniform_7-polytope
Shape with three equal sides
types of a triangle belong to the infinite family of n {\displaystyle n} -simplexes, with n = 2 {\displaystyle n=2} . Clifton Cathedral Dirichlet distribution
Equilateral_triangle
Prism with a 3-sided base
series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (equilateral triangles and squares in the case of the
Triangular_prism
Four-dimensional analog of the dodecahedron
unless it is all 5 vertices. It is impossible to rotate two concentric 4-simplexes with respect to each other such that some, but not all, of their vertices
120-cell
Generalization of a polytope in real space
construction as and quasiregular form as . All elements are simplexes. Real {3,4}, or , with 6 vertices, 12 edges, and 8 faces 2{3}2{4}3, or , with 9 vertices
Complex_polytope
TRUNCATED 6-SIMPLEXES
TRUNCATED 6-SIMPLEXES
Surname or Lastname
English and Irish (of Norman origin)
English and Irish (of Norman origin) : from the Old French personal name Picot, Pigot, a pet form of Pic (see Pike 6).
Female
Greek
(Θεοφάνια) Feminine form of Greek Theophanes, THEOPHANIA means "manifestation of God." This name used to be given to girls born on the Epiphany (January 6)--also called the 12th day of Christmas--which commemorates the visit of the three wise men (the Magi) to the infant Jesus.
Surname or Lastname
English
English : from the Middle English, Old French personal name Picot, Pigot, a pet form of Pic (see Pike 6). In Middle English, the form Piket (Old French Picquet) was also common.
Male
Japanese
(1-æš, 2-æ‚Ÿ, 3-è¡, 4-知, 5-覚, 6-è«, 7-了, 8-智) Japanese name SATORU means 1) "daybreak," 2) "enlightened," 3) "fast learner," 4) "knowledgeable," 5) "perceptive," 6) "persuasive," 7) "understanding," or 8) "wise."
Female
Japanese
(1-æµ, 2-æ…¶, 3-æ¡‚, 4-敬, 5-å•“, 6-åœ, 7-景) Japanese name KEI means 1) "blessed, lucky," 2) "happy," 3) "katsura tree," 4) "respectful," 5) "spring," 6) "square jewel," or "sunny."Â
Surname or Lastname
English (East Anglia, chiefly Norfolk)
English (East Anglia, chiefly Norfolk) : occupational name for someone who mowed pasture lands to provide hay, from an agent derivative of Middle English mow(en) ‘mow’ (Old English mÄwen).Welsh : nickname from mawr ‘big’ (see Moore 6).German (Möwer) : nickname from an agent derivative of Middle High German mÅven ‘to torment, trouble, or burden’.
Surname or Lastname
English
English : variant of Ayliff(e), which is from a Middle English personal name. In most cases, this is Old Norse EilÃfr ‘eternal life’, but it could also have absorbed the female name Ayleve (Old English Æ{dh}elgifu ‘noble gift’). It could also have absorbed a truncated form of Irish McAuliffe.
Male
Japanese
(1-晋, 2-信, 3-紳, 4-心, 5-慎, 6-新, 7-進, 8-真) Japanese name SHIN means 1) "advancing," 2) "belief," 3) "gentleman," 4) "heart," 5) "humble," 6) "new," 7) "progressive," and 8) "true." Compare with another form of Shin.
Surname or Lastname
English
English : variant spelling of Hain 1–3.German : variant spelling of Hain 4.Jewish : variant spelling of Hain 6.
Female
Japanese
(1-æ£, 2-é›…, 3-昌, 4-真, 5-政, 6-å°†) Unisex short form of Japanese names beginning with Masa-, MASA means 1) "correct, just," 2) "elegant," 3) "flourishing, prosperous" 4) "genuine, true," 5) "governing, political," 6) "military." Compare with strictly masculine Masa.
Surname or Lastname
English
English : from a pet form of the personal name William.Benjamin Wilmot and his wife, with their 6-year-old son William, emigrated from England to New Haven, CT, in or before 1640.
Boy/Male
Hindu, Indian, Tamil
Lord Muruga; Lord Vishnu; God with 6 Faces (Subrahmanyeswara Swamy)
Male
Japanese
(1-ç´€, 2-ä¿®, 3-ç†, 4-åŽ, 5-æ²», 6-çµ±) Japanese name OSAMU means 1) "chronicler," 2) "disciplined," 3) "logical," 4) "obtainer," 5) "to reign," 6) "ruler."
Surname or Lastname
English
English : possibly from Middle English Old French personal name Pic (see Pike 6) + the diminutive suffix -in.
Male
Japanese
(1-æ£, 2-é›…, 3-昌, 4-真, 5-政, 6-å°†) Unisex short form of Japanese names beginning with Masa-, MASA means 1) "correct, just," 2) "elegant, splendid" 3) "flourishing, prosperous" 4) "genuine, true," 5) "governing, political," 6) "military." Compare with another form of Masa.
Male
Hebrew
(שָׂרָף) Hebrew name SARAPH means "burning one" or "serpent." In the bible, this is the name of a son of Shelah. It is also the name of a species of venomous serpents mentioned in Numbers 21:6, and the name of an order of six-winged angels mentioned by Isaiah who attend upon God.
Surname or Lastname
English
English : unexplained; perhaps a variant of Tongs, itself a variant of Tong 6.Possibly an altered spelling of German Dungs, a variant of Dung.
Surname or Lastname
English (West Midlands)
English (West Midlands) : habitational name from any of the places called Harthill, named with Old English heorot ‘hart’ + hyll ‘hill’. There are several places of this name, for example in Cheshire, Derbyshire, and South Yorkshire, but apparently none in the West Midlands. It is also possible that the surname represents a truncated derivative of Hartlebury in Worcestershire. This place name derives from the Old English personal name Heortla + Old English burh ‘fort’.German : Americanized spelling of Hartel or Härtel.
Surname or Lastname
English (chiefly West Midlands)
English (chiefly West Midlands) : from the Middle English personal name Myat, formed from My, a truncated version of Mihel (an Old French form of Michael) + the diminutive suffix -at (from Old French -et, crossed with the originally pejorative Old French -ard).
Female
Japanese
(1-æµå, 2-æ…¶å, 3-æ¡‚å, 4-敬å, 5-å•“å, 6-åœå, 7-景å) Japanese name KEIKO means 1) "blessed, lucky child," 2) "happy child," 3) "katsura tree child," 4) "respectful child," 5) "spring child," 6) "square jewel child," or 7) "sunny child."
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