Polytope of Type {60,10}

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

Permutation Representation (Magma) :

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

References : None.
to this polytope