Emanuel Lodewijk Elte (16 March 1881 in
Amsterdam – 9 April 1943 in
Sobibór
Sobibor (, Polish: ) 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 ...
)
[ Emanuël Lodewijk Elte]
at joodsmonument.nl was a
Dutch mathematician. He is noted for discovering and classifying semiregular
polytopes 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) is a city and municipality in the Netherlands. It is the capital of the province of North Holland. Haarlem is situated at the northern edge of the Randstad, one of the most populated metropoli ...
. 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
Camp may refer to:
Outdoor accommodation and recreation
* Campsite or campground, a recreational outdoor sleeping and eating site
* a temporary settlement for nomads
* Camp, a term used in New England, Northern Ontario and New Brunswick to desc ...
, 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 concentration camp ( (); also or ) 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 con ...
.
[
]
Elte's semiregular polytopes of the first kind
His work rediscovered the finite semiregular polytopes of Thorold Gosset, 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, and renamed as a part of a larger class of uniform polytopes.[ 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
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the only r ...
= 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= 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
* Regional Currency Office
*Remote Communications Outlet
*Rifle combat optic
The Advanced Combat Optical Gunsight (ACOG) is a series of prism ...
, RID RID may refer to:
* Isaiah ben Mali di Trani (the Elder), an Italian Talmudist
* Radial immunodiffusion, a scientific technique for measuring the quantity of an antigen
* Radionuclide identification device, a hand-held instrument for the detecti ...
* Truncated quasiregular (omnitruncated
In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed.
It is a ''shortc ...
): 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 ord ...
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