Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór)[1] was a Dutchmathematician. 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. 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.[1]
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.[2] 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.[3] In the process he discovered all the main representatives of the exceptional En family of polytopes, save only 142 which did not satisfy his definition of semiregularity.
Summary of the semiregular polytopes of the first kind[4]
emanuel, lodewijk, elte, march, 1881, amsterdam, april, 1943, sobibór, dutch, mathematician, noted, discovering, classifying, semiregular, polytopes, dimensions, four, higher, elte, father, hartog, elte, headmaster, school, amsterdam, emanuel, elte, married, r. Emanuel Lodewijk Elte 16 March 1881 in Amsterdam 9 April 1943 in Sobibor 1 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 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 Sobibor where they were murdered his two children were murdered at Auschwitz 1 Elte s semiregular polytopes of the first kind EditHis 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 2 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 3 In the process he discovered all the main representatives of the exceptional En family of polytopes save only 142 which did not satisfy his definition of semiregularity Summary of the semiregular polytopes of the first kind 4 n Eltenotation Vertices Edges Faces Cells Facets Schlaflisymbol Coxetersymbol CoxeterdiagramPolyhedra Archimedean solids 3 tT 12 18 4p3 4p6 t 3 3 tC 24 36 6p8 8p3 t 4 3 tO 24 36 6p4 8p6 t 3 4 tD 60 90 20p3 12p10 t 5 3 tI 60 90 20p6 12p5 t 3 5 TT O 6 12 4 4 p3 r 3 3 31 1 011 CO 12 24 6p4 8p3 r 3 4 ID 30 60 20p3 12p5 r 3 5 Pq 2q 4q 2pq qp4 t 2 q APq 2q 4q 2pq 2qp3 s 2 2q semiregular 4 polytopes4 tC5 10 30 10 20 p3 5O 5T r 3 3 3 32 1 021 tC8 32 96 64p3 24p4 8CO 16T r 4 3 3 tC16 C24 48 96 96p3 16 8 O r 3 3 4 tC24 96 288 96p3 144p4 24CO 24C r 3 4 3 tC600 720 3600 1200 2400 p3 600O 120I r 3 3 5 tC120 1200 3600 2400p3 720p5 120ID 600T r 5 3 3 HM4 C16 8 24 32p3 8 8 T 3 31 1 111 30 60 20p3 20p6 5 5 tT 2t 3 3 3 288 576 192p3 144p8 24 24 tC 2t 3 4 3 20 60 40p3 30p4 10T 20P3 t0 3 3 3 3 144 576 384p3 288p4 48O 192P3 t0 3 3 4 3 q2 2q2 q2p4 2qpq q q Pq 2t q 2 q semiregular 5 polytopes5 S51 15 60 20 60 p3 30T 15O 6C5 6tC5 r 3 3 3 3 33 1 031 S52 20 90 120p3 30T 30O 6 6 C5 2r 3 3 3 3 32 2 022 HM5 16 80 160p3 80 40 T 16C5 10C16 3 32 1 121 Cr51 40 240 80 320 p3 160T 80O 32tC5 10C16 r 3 3 3 4 Cr52 80 480 320 320 p3 80T 200O 32tC5 10C24 2r 3 3 3 4 semiregular 6 polytopes6 S61 r 35 34 1 041 S62 2r 35 33 2 032 HM6 32 240 640p3 160 480 T 32S5 12HM5 3 33 1 131 V27 27 216 720p3 1080T 72S5 27HM5 3 3 32 1 221 V72 72 720 2160p3 2160T 27 27 HM6 3 32 2 122 semiregular 7 polytopes7 S71 r 36 35 1 051 S72 2r 36 34 2 042 S73 3r 36 33 3 033 HM7 64 672 2240p3 560 2240 T 64S6 14HM6 3 34 1 141 V56 56 756 4032p3 10080T 576S6 126Cr6 3 3 3 32 1 321 V126 126 2016 10080p3 20160T 576S6 56V27 3 3 33 1 231 V576 576 10080 40320p3 30240 20160 T 126HM6 56V72 3 33 2 132 semiregular 8 polytopes8 S81 r 37 36 1 061 S82 2r 37 35 2 052 S83 3r 37 34 3 043 HM8 128 1792 7168p3 1792 8960 T 128S7 16HM7 3 35 1 151 V2160 2160 69120 483840p3 1209600T 17280S7 240V126 3 3 34 1 241 V240 240 6720 60480p3 241920T 17280S7 2160Cr7 3 3 3 3 32 1 421 Added in this table as a sequence Elte recognized but did not enumerate explicitlyRegular dimensional families Sn n simplex S3 S4 S5 S6 S7 S8 Mn n cube measure polytope M3 M4 M5 M6 M7 M8 HMn n demicube half measure polytope HM3 HM4 M5 M6 HM7 HM8 Crn n orthoplex cross polytope Cr3 Cr4 Cr5 Cr6 Cr7 Cr8 Semiregular polytopes of first order Vn semiregular polytope with n verticesPolygons Pn regular n gonPolyhedra Regular T C O I D Truncated tT tC tO tI tD Quasiregular rectified CO ID Cantellated RCO RID Truncated quasiregular omnitruncated tCO tID Prismatic Pn APn4 polytopes Cn Regular 4 polytopes with n cells C5 C8 C16 C24 C120 C600 Rectified tC5 tC8 tC16 tC24 tC120 tC600See also EditGosset Elte figuresNotes Edit a b Emanuel Lodewijk Elte at joodsmonument nl Elte E L 1912 The Semiregular Polytopes of the Hyperspaces Groningen University of Groningen ISBN 1 4181 7968 X 1 2 Coxeter H S M Regular polytopes 3rd Edn Dover 1973 p 210 11 x Historical remarks Page 128 Retrieved from https en wikipedia org w index php title Emanuel Lodewijk Elte amp oldid 1059086137, wikipedia, wiki, book, books, library,
