Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*1200a
if this polytope has a name.
Group : SmallGroup(1200,513)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 50, 300, 100
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
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 : {6,6}*600a
   4-fold quotients : {6,3}*300
   75-fold quotients : {2,4}*16
   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)(  2,163)(  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);;
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*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)(  2,163)(  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);
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

References : None.
to this polytope