Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*1200a
if this polytope has a name.
Group : SmallGroup(1200,513)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 30, 300, 100
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,10}*600a
   4-fold quotients : {6,10}*300
   25-fold quotients : {6,4}*48a
   50-fold quotients : {6,2}*24
   75-fold quotients : {2,4}*16
   100-fold quotients : {3,2}*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,  7)(  8, 10)( 11, 13)( 14, 15)( 16, 19)( 17, 18)
( 21, 25)( 22, 24)( 26, 51)( 27, 55)( 28, 54)( 29, 53)( 30, 52)( 31, 57)
( 32, 56)( 33, 60)( 34, 59)( 35, 58)( 36, 63)( 37, 62)( 38, 61)( 39, 65)
( 40, 64)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 75)( 47, 74)
( 48, 73)( 49, 72)( 50, 71)( 77, 80)( 78, 79)( 81, 82)( 83, 85)( 86, 88)
( 89, 90)( 91, 94)( 92, 93)( 96,100)( 97, 99)(101,126)(102,130)(103,129)
(104,128)(105,127)(106,132)(107,131)(108,135)(109,134)(110,133)(111,138)
(112,137)(113,136)(114,140)(115,139)(116,144)(117,143)(118,142)(119,141)
(120,145)(121,150)(122,149)(123,148)(124,147)(125,146)(152,155)(153,154)
(156,157)(158,160)(161,163)(164,165)(166,169)(167,168)(171,175)(172,174)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,207)(182,206)(183,210)
(184,209)(185,208)(186,213)(187,212)(188,211)(189,215)(190,214)(191,219)
(192,218)(193,217)(194,216)(195,220)(196,225)(197,224)(198,223)(199,222)
(200,221)(227,230)(228,229)(231,232)(233,235)(236,238)(239,240)(241,244)
(242,243)(246,250)(247,249)(251,276)(252,280)(253,279)(254,278)(255,277)
(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)(262,287)(263,286)
(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)(270,295)(271,300)
(272,299)(273,298)(274,297)(275,296);;
s1 := (  1, 26)(  2, 50)(  3, 44)(  4, 38)(  5, 32)(  6, 31)(  7, 30)(  8, 49)
(  9, 43)( 10, 37)( 11, 36)( 12, 35)( 13, 29)( 14, 48)( 15, 42)( 16, 41)
( 17, 40)( 18, 34)( 19, 28)( 20, 47)( 21, 46)( 22, 45)( 23, 39)( 24, 33)
( 25, 27)( 52, 75)( 53, 69)( 54, 63)( 55, 57)( 58, 74)( 59, 68)( 60, 62)
( 64, 73)( 65, 67)( 70, 72)( 76,101)( 77,125)( 78,119)( 79,113)( 80,107)
( 81,106)( 82,105)( 83,124)( 84,118)( 85,112)( 86,111)( 87,110)( 88,104)
( 89,123)( 90,117)( 91,116)( 92,115)( 93,109)( 94,103)( 95,122)( 96,121)
( 97,120)( 98,114)( 99,108)(100,102)(127,150)(128,144)(129,138)(130,132)
(133,149)(134,143)(135,137)(139,148)(140,142)(145,147)(151,251)(152,275)
(153,269)(154,263)(155,257)(156,256)(157,255)(158,274)(159,268)(160,262)
(161,261)(162,260)(163,254)(164,273)(165,267)(166,266)(167,265)(168,259)
(169,253)(170,272)(171,271)(172,270)(173,264)(174,258)(175,252)(176,226)
(177,250)(178,244)(179,238)(180,232)(181,231)(182,230)(183,249)(184,243)
(185,237)(186,236)(187,235)(188,229)(189,248)(190,242)(191,241)(192,240)
(193,234)(194,228)(195,247)(196,246)(197,245)(198,239)(199,233)(200,227)
(201,276)(202,300)(203,294)(204,288)(205,282)(206,281)(207,280)(208,299)
(209,293)(210,287)(211,286)(212,285)(213,279)(214,298)(215,292)(216,291)
(217,290)(218,284)(219,278)(220,297)(221,296)(222,295)(223,289)(224,283)
(225,277);;
s2 := (  1,162)(  2,161)(  3,165)(  4,164)(  5,163)(  6,157)(  7,156)(  8,160)
(  9,159)( 10,158)( 11,152)( 12,151)( 13,155)( 14,154)( 15,153)( 16,172)
( 17,171)( 18,175)( 19,174)( 20,173)( 21,167)( 22,166)( 23,170)( 24,169)
( 25,168)( 26,187)( 27,186)( 28,190)( 29,189)( 30,188)( 31,182)( 32,181)
( 33,185)( 34,184)( 35,183)( 36,177)( 37,176)( 38,180)( 39,179)( 40,178)
( 41,197)( 42,196)( 43,200)( 44,199)( 45,198)( 46,192)( 47,191)( 48,195)
( 49,194)( 50,193)( 51,212)( 52,211)( 53,215)( 54,214)( 55,213)( 56,207)
( 57,206)( 58,210)( 59,209)( 60,208)( 61,202)( 62,201)( 63,205)( 64,204)
( 65,203)( 66,222)( 67,221)( 68,225)( 69,224)( 70,223)( 71,217)( 72,216)
( 73,220)( 74,219)( 75,218)( 76,237)( 77,236)( 78,240)( 79,239)( 80,238)
( 81,232)( 82,231)( 83,235)( 84,234)( 85,233)( 86,227)( 87,226)( 88,230)
( 89,229)( 90,228)( 91,247)( 92,246)( 93,250)( 94,249)( 95,248)( 96,242)
( 97,241)( 98,245)( 99,244)(100,243)(101,262)(102,261)(103,265)(104,264)
(105,263)(106,257)(107,256)(108,260)(109,259)(110,258)(111,252)(112,251)
(113,255)(114,254)(115,253)(116,272)(117,271)(118,275)(119,274)(120,273)
(121,267)(122,266)(123,270)(124,269)(125,268)(126,287)(127,286)(128,290)
(129,289)(130,288)(131,282)(132,281)(133,285)(134,284)(135,283)(136,277)
(137,276)(138,280)(139,279)(140,278)(141,297)(142,296)(143,300)(144,299)
(145,298)(146,292)(147,291)(148,295)(149,294)(150,293);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope