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Polytope of Type {100,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {100,6}*1200a
Also Known As : {100,6|2}. if this polytope has another name.
Group : SmallGroup(1200,131)
Rank : 3
Schlafli Type : {100,6}
Number of vertices, edges, etc : 100, 300, 6
Order of s0s1s2 : 300
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {50,6}*600
   3-fold quotients : {100,2}*400
   5-fold quotients : {20,6}*240a
   6-fold quotients : {50,2}*200
   10-fold quotients : {10,6}*120
   12-fold quotients : {25,2}*100
   15-fold quotients : {20,2}*80
   25-fold quotients : {4,6}*48a
   30-fold quotients : {10,2}*40
   50-fold quotients : {2,6}*24
   60-fold quotients : {5,2}*20
   75-fold quotients : {4,2}*16
   100-fold quotients : {2,3}*12
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)
( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)( 82, 99)
( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)
(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)
(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)(132,149)
(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)
(151,226)(152,230)(153,229)(154,228)(155,227)(156,250)(157,249)(158,248)
(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)
(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)(173,233)(174,232)
(175,231)(176,251)(177,255)(178,254)(179,253)(180,252)(181,275)(182,274)
(183,273)(184,272)(185,271)(186,270)(187,269)(188,268)(189,267)(190,266)
(191,265)(192,264)(193,263)(194,262)(195,261)(196,260)(197,259)(198,258)
(199,257)(200,256)(201,276)(202,280)(203,279)(204,278)(205,277)(206,300)
(207,299)(208,298)(209,297)(210,296)(211,295)(212,294)(213,293)(214,292)
(215,291)(216,290)(217,289)(218,288)(219,287)(220,286)(221,285)(222,284)
(223,283)(224,282)(225,281);;
s1 := (  1,156)(  2,160)(  3,159)(  4,158)(  5,157)(  6,151)(  7,155)(  8,154)
(  9,153)( 10,152)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)( 16,170)
( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)( 24,162)
( 25,161)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,201)( 32,205)
( 33,204)( 34,203)( 35,202)( 36,225)( 37,224)( 38,223)( 39,222)( 40,221)
( 41,220)( 42,219)( 43,218)( 44,217)( 45,216)( 46,215)( 47,214)( 48,213)
( 49,212)( 50,211)( 51,181)( 52,185)( 53,184)( 54,183)( 55,182)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,200)( 62,199)( 63,198)( 64,197)
( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,190)( 72,189)
( 73,188)( 74,187)( 75,186)( 76,231)( 77,235)( 78,234)( 79,233)( 80,232)
( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,250)( 87,249)( 88,248)
( 89,247)( 90,246)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)( 96,240)
( 97,239)( 98,238)( 99,237)(100,236)(101,281)(102,285)(103,284)(104,283)
(105,282)(106,276)(107,280)(108,279)(109,278)(110,277)(111,300)(112,299)
(113,298)(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)(120,291)
(121,290)(122,289)(123,288)(124,287)(125,286)(126,256)(127,260)(128,259)
(129,258)(130,257)(131,251)(132,255)(133,254)(134,253)(135,252)(136,275)
(137,274)(138,273)(139,272)(140,271)(141,270)(142,269)(143,268)(144,267)
(145,266)(146,265)(147,264)(148,263)(149,262)(150,261);;
s2 := (  1, 26)(  2, 27)(  3, 28)(  4, 29)(  5, 30)(  6, 31)(  7, 32)(  8, 33)
(  9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)( 16, 41)
( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)( 24, 49)
( 25, 50)( 76,101)( 77,102)( 78,103)( 79,104)( 80,105)( 81,106)( 82,107)
( 83,108)( 84,109)( 85,110)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)
( 91,116)( 92,117)( 93,118)( 94,119)( 95,120)( 96,121)( 97,122)( 98,123)
( 99,124)(100,125)(151,176)(152,177)(153,178)(154,179)(155,180)(156,181)
(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)(164,189)
(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)(172,197)
(173,198)(174,199)(175,200)(226,251)(227,252)(228,253)(229,254)(230,255)
(231,256)(232,257)(233,258)(234,259)(235,260)(236,261)(237,262)(238,263)
(239,264)(240,265)(241,266)(242,267)(243,268)(244,269)(245,270)(246,271)
(247,272)(248,273)(249,274)(250,275);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(300)!(  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)
(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)
(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)
(140,141)(151,226)(152,230)(153,229)(154,228)(155,227)(156,250)(157,249)
(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)
(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)(173,233)
(174,232)(175,231)(176,251)(177,255)(178,254)(179,253)(180,252)(181,275)
(182,274)(183,273)(184,272)(185,271)(186,270)(187,269)(188,268)(189,267)
(190,266)(191,265)(192,264)(193,263)(194,262)(195,261)(196,260)(197,259)
(198,258)(199,257)(200,256)(201,276)(202,280)(203,279)(204,278)(205,277)
(206,300)(207,299)(208,298)(209,297)(210,296)(211,295)(212,294)(213,293)
(214,292)(215,291)(216,290)(217,289)(218,288)(219,287)(220,286)(221,285)
(222,284)(223,283)(224,282)(225,281);
s1 := Sym(300)!(  1,156)(  2,160)(  3,159)(  4,158)(  5,157)(  6,151)(  7,155)
(  8,154)(  9,153)( 10,152)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)
( 16,170)( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)
( 24,162)( 25,161)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,201)
( 32,205)( 33,204)( 34,203)( 35,202)( 36,225)( 37,224)( 38,223)( 39,222)
( 40,221)( 41,220)( 42,219)( 43,218)( 44,217)( 45,216)( 46,215)( 47,214)
( 48,213)( 49,212)( 50,211)( 51,181)( 52,185)( 53,184)( 54,183)( 55,182)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,200)( 62,199)( 63,198)
( 64,197)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,190)
( 72,189)( 73,188)( 74,187)( 75,186)( 76,231)( 77,235)( 78,234)( 79,233)
( 80,232)( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,250)( 87,249)
( 88,248)( 89,247)( 90,246)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)
( 96,240)( 97,239)( 98,238)( 99,237)(100,236)(101,281)(102,285)(103,284)
(104,283)(105,282)(106,276)(107,280)(108,279)(109,278)(110,277)(111,300)
(112,299)(113,298)(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)
(120,291)(121,290)(122,289)(123,288)(124,287)(125,286)(126,256)(127,260)
(128,259)(129,258)(130,257)(131,251)(132,255)(133,254)(134,253)(135,252)
(136,275)(137,274)(138,273)(139,272)(140,271)(141,270)(142,269)(143,268)
(144,267)(145,266)(146,265)(147,264)(148,263)(149,262)(150,261);
s2 := Sym(300)!(  1, 26)(  2, 27)(  3, 28)(  4, 29)(  5, 30)(  6, 31)(  7, 32)
(  8, 33)(  9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)
( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)
( 24, 49)( 25, 50)( 76,101)( 77,102)( 78,103)( 79,104)( 80,105)( 81,106)
( 82,107)( 83,108)( 84,109)( 85,110)( 86,111)( 87,112)( 88,113)( 89,114)
( 90,115)( 91,116)( 92,117)( 93,118)( 94,119)( 95,120)( 96,121)( 97,122)
( 98,123)( 99,124)(100,125)(151,176)(152,177)(153,178)(154,179)(155,180)
(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)
(164,189)(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)
(172,197)(173,198)(174,199)(175,200)(226,251)(227,252)(228,253)(229,254)
(230,255)(231,256)(232,257)(233,258)(234,259)(235,260)(236,261)(237,262)
(238,263)(239,264)(240,265)(241,266)(242,267)(243,268)(244,269)(245,270)
(246,271)(247,272)(248,273)(249,274)(250,275);
poly := sub<Sym(300)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope