Polytope of Type {6,12}

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

References : None.
to this polytope