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Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*1200a
if this polytope has a name.
Group : SmallGroup(1200,513)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 100, 300, 30
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6}*600a
   4-fold quotients : {10,6}*300
   25-fold quotients : {4,6}*48a
   50-fold quotients : {2,6}*24
   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, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(151,226)(152,230)(153,229)(154,228)(155,227)(156,246)(157,250)(158,249)
(159,248)(160,247)(161,241)(162,245)(163,244)(164,243)(165,242)(166,236)
(167,240)(168,239)(169,238)(170,237)(171,231)(172,235)(173,234)(174,233)
(175,232)(176,251)(177,255)(178,254)(179,253)(180,252)(181,271)(182,275)
(183,274)(184,273)(185,272)(186,266)(187,270)(188,269)(189,268)(190,267)
(191,261)(192,265)(193,264)(194,263)(195,262)(196,256)(197,260)(198,259)
(199,258)(200,257)(201,276)(202,280)(203,279)(204,278)(205,277)(206,296)
(207,300)(208,299)(209,298)(210,297)(211,291)(212,295)(213,294)(214,293)
(215,292)(216,286)(217,290)(218,289)(219,288)(220,287)(221,281)(222,285)
(223,284)(224,283)(225,282);;
s1 := (  1,162)(  2,163)(  3,164)(  4,165)(  5,161)(  6,156)(  7,157)(  8,158)
(  9,159)( 10,160)( 11,155)( 12,151)( 13,152)( 14,153)( 15,154)( 16,174)
( 17,175)( 18,171)( 19,172)( 20,173)( 21,168)( 22,169)( 23,170)( 24,166)
( 25,167)( 26,212)( 27,213)( 28,214)( 29,215)( 30,211)( 31,206)( 32,207)
( 33,208)( 34,209)( 35,210)( 36,205)( 37,201)( 38,202)( 39,203)( 40,204)
( 41,224)( 42,225)( 43,221)( 44,222)( 45,223)( 46,218)( 47,219)( 48,220)
( 49,216)( 50,217)( 51,187)( 52,188)( 53,189)( 54,190)( 55,186)( 56,181)
( 57,182)( 58,183)( 59,184)( 60,185)( 61,180)( 62,176)( 63,177)( 64,178)
( 65,179)( 66,199)( 67,200)( 68,196)( 69,197)( 70,198)( 71,193)( 72,194)
( 73,195)( 74,191)( 75,192)( 76,237)( 77,238)( 78,239)( 79,240)( 80,236)
( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,230)( 87,226)( 88,227)
( 89,228)( 90,229)( 91,249)( 92,250)( 93,246)( 94,247)( 95,248)( 96,243)
( 97,244)( 98,245)( 99,241)(100,242)(101,287)(102,288)(103,289)(104,290)
(105,286)(106,281)(107,282)(108,283)(109,284)(110,285)(111,280)(112,276)
(113,277)(114,278)(115,279)(116,299)(117,300)(118,296)(119,297)(120,298)
(121,293)(122,294)(123,295)(124,291)(125,292)(126,262)(127,263)(128,264)
(129,265)(130,261)(131,256)(132,257)(133,258)(134,259)(135,260)(136,255)
(137,251)(138,252)(139,253)(140,254)(141,274)(142,275)(143,271)(144,272)
(145,273)(146,268)(147,269)(148,270)(149,266)(150,267);;
s2 := (  1, 26)(  2, 32)(  3, 38)(  4, 44)(  5, 50)(  6, 46)(  7, 27)(  8, 33)
(  9, 39)( 10, 45)( 11, 41)( 12, 47)( 13, 28)( 14, 34)( 15, 40)( 16, 36)
( 17, 42)( 18, 48)( 19, 29)( 20, 35)( 21, 31)( 22, 37)( 23, 43)( 24, 49)
( 25, 30)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)
( 61, 66)( 62, 72)( 68, 73)( 76,101)( 77,107)( 78,113)( 79,119)( 80,125)
( 81,121)( 82,102)( 83,108)( 84,114)( 85,120)( 86,116)( 87,122)( 88,103)
( 89,109)( 90,115)( 91,111)( 92,117)( 93,123)( 94,104)( 95,110)( 96,106)
( 97,112)( 98,118)( 99,124)(100,105)(127,132)(128,138)(129,144)(130,150)
(131,146)(134,139)(135,145)(136,141)(137,147)(143,148)(151,176)(152,182)
(153,188)(154,194)(155,200)(156,196)(157,177)(158,183)(159,189)(160,195)
(161,191)(162,197)(163,178)(164,184)(165,190)(166,186)(167,192)(168,198)
(169,179)(170,185)(171,181)(172,187)(173,193)(174,199)(175,180)(202,207)
(203,213)(204,219)(205,225)(206,221)(209,214)(210,220)(211,216)(212,222)
(218,223)(226,251)(227,257)(228,263)(229,269)(230,275)(231,271)(232,252)
(233,258)(234,264)(235,270)(236,266)(237,272)(238,253)(239,259)(240,265)
(241,261)(242,267)(243,273)(244,254)(245,260)(246,256)(247,262)(248,268)
(249,274)(250,255)(277,282)(278,288)(279,294)(280,300)(281,296)(284,289)
(285,295)(286,291)(287,297)(293,298);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*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, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(151,226)(152,230)(153,229)(154,228)(155,227)(156,246)(157,250)
(158,249)(159,248)(160,247)(161,241)(162,245)(163,244)(164,243)(165,242)
(166,236)(167,240)(168,239)(169,238)(170,237)(171,231)(172,235)(173,234)
(174,233)(175,232)(176,251)(177,255)(178,254)(179,253)(180,252)(181,271)
(182,275)(183,274)(184,273)(185,272)(186,266)(187,270)(188,269)(189,268)
(190,267)(191,261)(192,265)(193,264)(194,263)(195,262)(196,256)(197,260)
(198,259)(199,258)(200,257)(201,276)(202,280)(203,279)(204,278)(205,277)
(206,296)(207,300)(208,299)(209,298)(210,297)(211,291)(212,295)(213,294)
(214,293)(215,292)(216,286)(217,290)(218,289)(219,288)(220,287)(221,281)
(222,285)(223,284)(224,283)(225,282);
s1 := Sym(300)!(  1,162)(  2,163)(  3,164)(  4,165)(  5,161)(  6,156)(  7,157)
(  8,158)(  9,159)( 10,160)( 11,155)( 12,151)( 13,152)( 14,153)( 15,154)
( 16,174)( 17,175)( 18,171)( 19,172)( 20,173)( 21,168)( 22,169)( 23,170)
( 24,166)( 25,167)( 26,212)( 27,213)( 28,214)( 29,215)( 30,211)( 31,206)
( 32,207)( 33,208)( 34,209)( 35,210)( 36,205)( 37,201)( 38,202)( 39,203)
( 40,204)( 41,224)( 42,225)( 43,221)( 44,222)( 45,223)( 46,218)( 47,219)
( 48,220)( 49,216)( 50,217)( 51,187)( 52,188)( 53,189)( 54,190)( 55,186)
( 56,181)( 57,182)( 58,183)( 59,184)( 60,185)( 61,180)( 62,176)( 63,177)
( 64,178)( 65,179)( 66,199)( 67,200)( 68,196)( 69,197)( 70,198)( 71,193)
( 72,194)( 73,195)( 74,191)( 75,192)( 76,237)( 77,238)( 78,239)( 79,240)
( 80,236)( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,230)( 87,226)
( 88,227)( 89,228)( 90,229)( 91,249)( 92,250)( 93,246)( 94,247)( 95,248)
( 96,243)( 97,244)( 98,245)( 99,241)(100,242)(101,287)(102,288)(103,289)
(104,290)(105,286)(106,281)(107,282)(108,283)(109,284)(110,285)(111,280)
(112,276)(113,277)(114,278)(115,279)(116,299)(117,300)(118,296)(119,297)
(120,298)(121,293)(122,294)(123,295)(124,291)(125,292)(126,262)(127,263)
(128,264)(129,265)(130,261)(131,256)(132,257)(133,258)(134,259)(135,260)
(136,255)(137,251)(138,252)(139,253)(140,254)(141,274)(142,275)(143,271)
(144,272)(145,273)(146,268)(147,269)(148,270)(149,266)(150,267);
s2 := Sym(300)!(  1, 26)(  2, 32)(  3, 38)(  4, 44)(  5, 50)(  6, 46)(  7, 27)
(  8, 33)(  9, 39)( 10, 45)( 11, 41)( 12, 47)( 13, 28)( 14, 34)( 15, 40)
( 16, 36)( 17, 42)( 18, 48)( 19, 29)( 20, 35)( 21, 31)( 22, 37)( 23, 43)
( 24, 49)( 25, 30)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)
( 60, 70)( 61, 66)( 62, 72)( 68, 73)( 76,101)( 77,107)( 78,113)( 79,119)
( 80,125)( 81,121)( 82,102)( 83,108)( 84,114)( 85,120)( 86,116)( 87,122)
( 88,103)( 89,109)( 90,115)( 91,111)( 92,117)( 93,123)( 94,104)( 95,110)
( 96,106)( 97,112)( 98,118)( 99,124)(100,105)(127,132)(128,138)(129,144)
(130,150)(131,146)(134,139)(135,145)(136,141)(137,147)(143,148)(151,176)
(152,182)(153,188)(154,194)(155,200)(156,196)(157,177)(158,183)(159,189)
(160,195)(161,191)(162,197)(163,178)(164,184)(165,190)(166,186)(167,192)
(168,198)(169,179)(170,185)(171,181)(172,187)(173,193)(174,199)(175,180)
(202,207)(203,213)(204,219)(205,225)(206,221)(209,214)(210,220)(211,216)
(212,222)(218,223)(226,251)(227,257)(228,263)(229,269)(230,275)(231,271)
(232,252)(233,258)(234,264)(235,270)(236,266)(237,272)(238,253)(239,259)
(240,265)(241,261)(242,267)(243,273)(244,254)(245,260)(246,256)(247,262)
(248,268)(249,274)(250,255)(277,282)(278,288)(279,294)(280,300)(281,296)
(284,289)(285,295)(286,291)(287,297)(293,298);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope