Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*1200b
if this polytope has a name.
Group : SmallGroup(1200,522)
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}*600b
   4-fold quotients : {10,3}*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 := (  1,152)(  2,151)(  3,155)(  4,154)(  5,153)(  6,158)(  7,157)(  8,156)
(  9,160)( 10,159)( 11,164)( 12,163)( 13,162)( 14,161)( 15,165)( 16,170)
( 17,169)( 18,168)( 19,167)( 20,166)( 21,171)( 22,175)( 23,174)( 24,173)
( 25,172)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,208)( 32,207)
( 33,206)( 34,210)( 35,209)( 36,214)( 37,213)( 38,212)( 39,211)( 40,215)
( 41,220)( 42,219)( 43,218)( 44,217)( 45,216)( 46,221)( 47,225)( 48,224)
( 49,223)( 50,222)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)( 56,183)
( 57,182)( 58,181)( 59,185)( 60,184)( 61,189)( 62,188)( 63,187)( 64,186)
( 65,190)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,196)( 72,200)
( 73,199)( 74,198)( 75,197)( 76,227)( 77,226)( 78,230)( 79,229)( 80,228)
( 81,233)( 82,232)( 83,231)( 84,235)( 85,234)( 86,239)( 87,238)( 88,237)
( 89,236)( 90,240)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)( 96,246)
( 97,250)( 98,249)( 99,248)(100,247)(101,277)(102,276)(103,280)(104,279)
(105,278)(106,283)(107,282)(108,281)(109,285)(110,284)(111,289)(112,288)
(113,287)(114,286)(115,290)(116,295)(117,294)(118,293)(119,292)(120,291)
(121,296)(122,300)(123,299)(124,298)(125,297)(126,252)(127,251)(128,255)
(129,254)(130,253)(131,258)(132,257)(133,256)(134,260)(135,259)(136,264)
(137,263)(138,262)(139,261)(140,265)(141,270)(142,269)(143,268)(144,267)
(145,266)(146,271)(147,275)(148,274)(149,273)(150,272);;
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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, 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)!(  1,152)(  2,151)(  3,155)(  4,154)(  5,153)(  6,158)(  7,157)
(  8,156)(  9,160)( 10,159)( 11,164)( 12,163)( 13,162)( 14,161)( 15,165)
( 16,170)( 17,169)( 18,168)( 19,167)( 20,166)( 21,171)( 22,175)( 23,174)
( 24,173)( 25,172)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,208)
( 32,207)( 33,206)( 34,210)( 35,209)( 36,214)( 37,213)( 38,212)( 39,211)
( 40,215)( 41,220)( 42,219)( 43,218)( 44,217)( 45,216)( 46,221)( 47,225)
( 48,224)( 49,223)( 50,222)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)
( 56,183)( 57,182)( 58,181)( 59,185)( 60,184)( 61,189)( 62,188)( 63,187)
( 64,186)( 65,190)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,196)
( 72,200)( 73,199)( 74,198)( 75,197)( 76,227)( 77,226)( 78,230)( 79,229)
( 80,228)( 81,233)( 82,232)( 83,231)( 84,235)( 85,234)( 86,239)( 87,238)
( 88,237)( 89,236)( 90,240)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)
( 96,246)( 97,250)( 98,249)( 99,248)(100,247)(101,277)(102,276)(103,280)
(104,279)(105,278)(106,283)(107,282)(108,281)(109,285)(110,284)(111,289)
(112,288)(113,287)(114,286)(115,290)(116,295)(117,294)(118,293)(119,292)
(120,291)(121,296)(122,300)(123,299)(124,298)(125,297)(126,252)(127,251)
(128,255)(129,254)(130,253)(131,258)(132,257)(133,256)(134,260)(135,259)
(136,264)(137,263)(138,262)(139,261)(140,265)(141,270)(142,269)(143,268)
(144,267)(145,266)(146,271)(147,275)(148,274)(149,273)(150,272);
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope