Emanuel Lodewijk Elte (16 March 1881 in
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...
– 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
Dutch commonly refers to:
* Something of, from, or related to the Netherlands
* Dutch people ()
* Dutch language ()
Dutch may also refer to:
Places
* Dutch, West Virginia, a community in the United States
* Pennsylvania Dutch Country
People E ...
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, structure, space, models, and change.
History
On ...
. 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 -d ...
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) 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, 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 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 Polytop ...
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, and ...
, and further allowing not only regular facets
A facet is a flat surface of a geometric shape, e.g., of a cut gemstone.
Facet may also refer to:
Arts, entertainment, and media
* ''Facets'' (album), an album by Jim Croce
* ''Facets'', a 1980 album by jazz pianist Monty Alexander and his tri ...
, 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 and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.
Biography
Coxeter was born in Kensington to ...
, 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 facets. The uniform polytopes in two dimensions are the regular polygons (the definition is different in 2 dimensions to exclude vert ...
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
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
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular Pyramid (geometry), pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex ( ...
= 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, or cocube is a regular, convex polytope that exists in ''n''- dimensional Euclidean space. A 2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahed ...
= 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
*Royal College of Organists
*Royal Concertgebouw Orchestra
The Roy ...
, 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): 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
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