Polytope of Type {12,6}

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

References : None.
to this polytope