simplicialadj.

Brit.

/sɪmˈplɪʃl/, U.S.

/sɪmˈplɪʃəl/

Origin: A borrowing from German. Etymon: German simplizial.

Etymology: < German simplizial (1912 or earlier) < classical Latin simplic- , simplex single (see simplex adj. and n., and compare simplex n. 2) + German -ial -ial suffix.

Mathematics.

Of, relating to, or involving simplices (simplex n. 2). Also: that is a simplex.

ΘΚΠ

the world > relative properties > number > geometry > shape or figure > [adjective] > having specific property

hypotenusal?a1560

oblique?a1560

local1673

focal1676

octantal1777

symmetrical1794

radical1848

self-conjugate1855

quadric1856

stellated1859

periphractic1881

homoeoidal1883

tridiametral1891

one-sided1893

semi-infinite1903

simplicial1913

mirror-symmetric1952

1913 Proc. Section Sci. Koninklijke Akad. van Wetenschappen te Amsterdam 15 i. 121 We have two different net fragments..limited by the same simplicial approximation.

1926 Trans. Amer. Math. Soc. 28 3 Such a C_n is the homeomorph of an n-dimensional polyhedron..whose faces are all simplicial cells.

1976 European Econ. Rev. 8 305 The simplicial sub-division methods modelled by Scarf (1973) can be replaced by quicker Newton methods.

2006 J. McCleary First Course Topol. xi. 183 It is possible to define linear mappings that do not necessarily come from a simplicial mapping.

Compounds

simplicial complex n. a set of points, lines, triangles, tetrahedrons, and higher-dimensional simplices that satisfies certain criteria.In a simplicial complex, each simplex which is a vertex, edge, or face, etc., of a simplex included in the complex must also be an element of the complex in its own right. Also, the intersection of two simplices must itself be a simplex, such as a vertex or edge, that is shared by both.

ΚΠ

1930 Ann. Math. 31 276 We can then take for H_r a simplicial complex.

1963 Canad. Jrnl. Math. 15 592 A triangulated 3-sphere is a finite, simplicial complex whose geometric realization is homeomorphic to a 3-sphere.

2014 H. Edelsbrunner Short Course Computational Geom. & Topol. x. 73 It is often convenient to talk about a simplicial complex abstractly, without reference to its realization in Euclidean space.

This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022).

单词	simplicial
释义	simplicialadj. Brit. /sɪmˈplɪʃl/, U.S. /sɪmˈplɪʃəl/ Origin: A borrowing from German. Etymon: German simplizial. Etymology: < German simplizial (1912 or earlier) < classical Latin simplic- , simplex single (see simplex adj. and n., and compare simplex n. 2) + German -ial -ial suffix. Mathematics. Of, relating to, or involving simplices (simplex n. 2). Also: that is a simplex. ΘΚΠ the world > relative properties > number > geometry > shape or figure > [adjective] > having specific property hypotenusal?a1560 oblique?a1560 local1673 focal1676 octantal1777 symmetrical1794 radical1848 self-conjugate1855 quadric1856 stellated1859 periphractic1881 homoeoidal1883 tridiametral1891 one-sided1893 semi-infinite1903 simplicial1913 mirror-symmetric1952 1913 Proc. Section Sci. Koninklijke Akad. van Wetenschappen te Amsterdam 15 i. 121 We have two different net fragments..limited by the same simplicial approximation. 1926 Trans. Amer. Math. Soc. 28 3 Such a C_n is the homeomorph of an n-dimensional polyhedron..whose faces are all simplicial cells. 1976 European Econ. Rev. 8 305 The simplicial sub-division methods modelled by Scarf (1973) can be replaced by quicker Newton methods. 2006 J. McCleary First Course Topol. xi. 183 It is possible to define linear mappings that do not necessarily come from a simplicial mapping. Compounds simplicial complex n. a set of points, lines, triangles, tetrahedrons, and higher-dimensional simplices that satisfies certain criteria.In a simplicial complex, each simplex which is a vertex, edge, or face, etc., of a simplex included in the complex must also be an element of the complex in its own right. Also, the intersection of two simplices must itself be a simplex, such as a vertex or edge, that is shared by both. ΚΠ 1930 Ann. Math. 31 276 We can then take for H_r a simplicial complex. 1963 Canad. Jrnl. Math. 15 592 A triangulated 3-sphere is a finite, simplicial complex whose geometric realization is homeomorphic to a 3-sphere. 2014 H. Edelsbrunner Short Course Computational Geom. & Topol. x. 73 It is often convenient to talk about a simplicial complex abstractly, without reference to its realization in Euclidean space. This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022). < adj.1913
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