Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1200b
if this polytope has a name.
Group : SmallGroup(1200,522)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 100, 300, 50
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
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 : {6,6}*600a
   4-fold quotients : {6,3}*300
   75-fold quotients : {4,2}*16
   150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope