Emanuel Lodewijk Elte (16 March 1881 in
Amsterdam
Amsterdam ( , ; ; ) is the capital of the Netherlands, capital and Municipalities of the Netherlands, largest city of the Kingdom of the Netherlands. It has a population of 933,680 in June 2024 within the city proper, 1,457,018 in the City Re ...
– 9 April 1943 in
Sobibór
Sobibor ( ; ) was an extermination camp built and operated by Nazi Germany as part of Operation Reinhard. It was located in the forest near the village of Żłobek Duży in the General Government region of German-occupied Poland.
As an exte ...
)
[ Emanuël Lodewijk Elte]
at joodsmonument.nl was a
Dutch
Dutch or Nederlands commonly refers to:
* Something of, from, or related to the Netherlands
** Dutch people as an ethnic group ()
** Dutch nationality law, history and regulations of Dutch citizenship ()
** Dutch language ()
* In specific terms, i ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. He is noted for discovering and classifying semiregular
polytope
In elementary geometry, a polytope is a geometric object with flat sides ('' faces''). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an ...
s in dimensions four and higher.
Elte's father Hartog Elte was headmaster of a school in Amsterdam. Emanuel Elte married Rebecca Stork in 1912 in Amsterdam, when he was a teacher at a high school in that city. By 1943 the family lived in
Haarlem
Haarlem (; predecessor of ''Harlem'' in English language, English) is a List of cities in the Netherlands by province, city and Municipalities of the Netherlands, municipality in the Netherlands. It is the capital of the Provinces of the Nether ...
. When on January 30 of that year a German officer was shot in that town, in reprisal a hundred inhabitants of Haarlem were transported to the
Camp Vught, including Elte and his family. As Jews, he and his wife were further deported to Sobibór, where they were murdered; his two children were murdered at
Auschwitz
Auschwitz, or Oświęcim, was a complex of over 40 concentration and extermination camps operated by Nazi Germany in occupied Poland (in a portion annexed into Germany in 1939) during World War II and the Holocaust. It consisted of Auschw ...
.
[
]
Elte's semiregular polytopes of the first kind
His work rediscovered the finite semiregular polytope
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-transitive and has all its facets being regular polytopes. E.L. Elte compiled a longer list in 1912 as ''The Semiregular Polyto ...
s of Thorold Gosset
John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher, a ...
, and further allowing not only regular facets, but recursively also allowing one or two semiregular ones. These were enumerated in his 1912 book, ''The Semiregular Polytopes of the Hyperspaces''. He called them ''semiregular polytopes of the first kind'', limiting his search to one or two types of regular or semiregular ''k''-faces. These polytopes and more were rediscovered again by Coxeter
Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician. He is regarded as one of the greatest geometers of the 20th century.
Coxeter was born in England and educated ...
, and renamed as a part of a larger class of uniform polytope
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform Facet (mathematics), facets. Here, "vertex-transitive" means that it has symmetries taking every vertex to every other vertex; the sam ...
s.[ Coxeter, H.S.M. ''Regular polytopes'', 3rd Edn, Dover (1973) p. 210 (11.x Historical remarks)] In the process he discovered all the main representatives of the exceptional E''n'' family of polytopes, save only 142 which did not satisfy his definition of semiregularity.
:(*) Added in this table as a sequence Elte recognized but did not enumerate explicitly
Regular dimensional families:
* ''S''''n'' = ''n''-simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
: S3, S4, S5, S6, S7, S8, ...
* ''M''''n'' = ''n''-cube
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...
= measure polytope: ''M''3, ''M''4, ''M''5, ''M''6, ''M''7, ''M''8, ...
* ''HM''''n'' = ''n''- demicube= half-measure polytope: ''HM''3, ''HM''4, ''M''5, ''M''6, ''HM''7, ''HM''8, ...
* ''Cr''''n'' = ''n''-orthoplex
In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular polytope, regular, convex polytope that exists in ''n''-dimensions, dimensional Euclidean space. A 2-dimensional cross-polytope is a square, a 3-dimensi ...
= cross polytope: ''Cr''3, ''Cr''4, ''Cr''5, ''Cr''6, ''Cr''7, ''Cr''8, ...
Semiregular polytopes of first order:
* ''V''''n'' = semiregular polytope with ''n'' vertices
Polygons
* ''P''''n'' = regular ''n''-gon
Polyhedra:
* Regular: T, C, O, I, D
* Truncated: tT, tC, tO, tI, tD
* Quasiregular (rectified): CO, ID
* Cantellated: RCO RCO may refer to:
*Air Force Rapid Capabilities Office
* Recovery Consistency Objective, in computing
* Refugee-led Community Organisation
* Regional Currency Office
*Remote Communications Outlet
*Rifle combat optic
*Royal College of Organists
*Ro ...
, RID
* Truncated quasiregular (omnitruncated
In geometry, an omnitruncation of a convex polytope is a simple polytope of the same dimension, having a vertex for each Flag (geometry), flag of the original polytope and a Facet (geometry), facet for each face of any dimension of the original pol ...
): tCO, tID
* Prismatic: Pn, AP''n''
4-polytopes:
* ''C''''n'' = Regular 4-polytopes with ''n'' cells: C5, C8, C16, C24, C120, C600
* Rectified: tC5, tC8, tC16, tC24, tC120, tC600
See also
* Gosset–Elte figures
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular polytopes, regular, generated by a Wythoff construction with mirrors all related by order-2 and or ...
Notes
{{DEFAULTSORT:Elte, E. L.
1881 births
1943 deaths
Dutch mathematicians
Dutch Jews who died in the Holocaust
Scientists from Amsterdam
Dutch people who died in Sobibor extermination camp
Dutch civilians killed in World War II