Polytope of Type {60,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,10}*1200b
Also Known As : {60,10|2}. if this polytope has another name.
Group : SmallGroup(1200,842)
Rank : 3
Schlafli Type : {60,10}
Number of vertices, edges, etc : 60, 300, 10
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {30,10}*600b
   3-fold quotients : {20,10}*400a
   5-fold quotients : {12,10}*240, {60,2}*240
   6-fold quotients : {10,10}*200a
   10-fold quotients : {6,10}*120, {30,2}*120
   15-fold quotients : {20,2}*80, {4,10}*80
   20-fold quotients : {15,2}*60
   25-fold quotients : {12,2}*48
   30-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {6,2}*24
   60-fold quotients : {2,5}*20, {5,2}*20
   75-fold quotients : {4,2}*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 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)( 31, 71)
( 32, 72)( 33, 73)( 34, 74)( 35, 75)( 36, 66)( 37, 67)( 38, 68)( 39, 69)
( 40, 70)( 41, 61)( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 56)( 47, 57)
( 48, 58)( 49, 59)( 50, 60)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)
( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(101,126)(102,127)(103,128)
(104,129)(105,130)(106,146)(107,147)(108,148)(109,149)(110,150)(111,141)
(112,142)(113,143)(114,144)(115,145)(116,136)(117,137)(118,138)(119,139)
(120,140)(121,131)(122,132)(123,133)(124,134)(125,135)(151,226)(152,227)
(153,228)(154,229)(155,230)(156,246)(157,247)(158,248)(159,249)(160,250)
(161,241)(162,242)(163,243)(164,244)(165,245)(166,236)(167,237)(168,238)
(169,239)(170,240)(171,231)(172,232)(173,233)(174,234)(175,235)(176,276)
(177,277)(178,278)(179,279)(180,280)(181,296)(182,297)(183,298)(184,299)
(185,300)(186,291)(187,292)(188,293)(189,294)(190,295)(191,286)(192,287)
(193,288)(194,289)(195,290)(196,281)(197,282)(198,283)(199,284)(200,285)
(201,251)(202,252)(203,253)(204,254)(205,255)(206,271)(207,272)(208,273)
(209,274)(210,275)(211,266)(212,267)(213,268)(214,269)(215,270)(216,261)
(217,262)(218,263)(219,264)(220,265)(221,256)(222,257)(223,258)(224,259)
(225,260);;
s1 := (  1,181)(  2,185)(  3,184)(  4,183)(  5,182)(  6,176)(  7,180)(  8,179)
(  9,178)( 10,177)( 11,196)( 12,200)( 13,199)( 14,198)( 15,197)( 16,191)
( 17,195)( 18,194)( 19,193)( 20,192)( 21,186)( 22,190)( 23,189)( 24,188)
( 25,187)( 26,156)( 27,160)( 28,159)( 29,158)( 30,157)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,171)( 37,175)( 38,174)( 39,173)( 40,172)
( 41,166)( 42,170)( 43,169)( 44,168)( 45,167)( 46,161)( 47,165)( 48,164)
( 49,163)( 50,162)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)( 56,201)
( 57,205)( 58,204)( 59,203)( 60,202)( 61,221)( 62,225)( 63,224)( 64,223)
( 65,222)( 66,216)( 67,220)( 68,219)( 69,218)( 70,217)( 71,211)( 72,215)
( 73,214)( 74,213)( 75,212)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,271)( 87,275)( 88,274)
( 89,273)( 90,272)( 91,266)( 92,270)( 93,269)( 94,268)( 95,267)( 96,261)
( 97,265)( 98,264)( 99,263)(100,262)(101,231)(102,235)(103,234)(104,233)
(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,246)(112,250)
(113,249)(114,248)(115,247)(116,241)(117,245)(118,244)(119,243)(120,242)
(121,236)(122,240)(123,239)(124,238)(125,237)(126,281)(127,285)(128,284)
(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)(136,296)
(137,300)(138,299)(139,298)(140,297)(141,291)(142,295)(143,294)(144,293)
(145,292)(146,286)(147,290)(148,289)(149,288)(150,287);;
s2 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)
(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)
(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)
(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)
(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)(198,200)
(201,202)(203,205)(206,207)(208,210)(211,212)(213,215)(216,217)(218,220)
(221,222)(223,225)(226,227)(228,230)(231,232)(233,235)(236,237)(238,240)
(241,242)(243,245)(246,247)(248,250)(251,252)(253,255)(256,257)(258,260)
(261,262)(263,265)(266,267)(268,270)(271,272)(273,275)(276,277)(278,280)
(281,282)(283,285)(286,287)(288,290)(291,292)(293,295)(296,297)(298,300);;
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*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*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*s1*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*s1*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*s1*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope