Polytope of Type {10,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,60}*1200b
Also Known As : {10,60|2}. if this polytope has another name.
Group : SmallGroup(1200,842)
Rank : 3
Schlafli Type : {10,60}
Number of vertices, edges, etc : 10, 300, 60
Order of s0s1s2 : 60
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {10,30}*600b
3-fold quotients : {10,20}*400a
5-fold quotients : {10,12}*240, {2,60}*240
6-fold quotients : {10,10}*200a
10-fold quotients : {10,6}*120, {2,30}*120
15-fold quotients : {2,20}*80, {10,4}*80
20-fold quotients : {2,15}*60
25-fold quotients : {2,12}*48
30-fold quotients : {2,10}*40, {10,2}*40
50-fold quotients : {2,6}*24
60-fold quotients : {2,5}*20, {5,2}*20
75-fold quotients : {2,4}*16
100-fold quotients : {2,3}*12
150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 52)( 27, 51)( 28, 55)( 29, 54)
( 30, 53)( 31, 72)( 32, 71)( 33, 75)( 34, 74)( 35, 73)( 36, 67)( 37, 66)
( 38, 70)( 39, 69)( 40, 68)( 41, 62)( 42, 61)( 43, 65)( 44, 64)( 45, 63)
( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 76, 77)( 78, 80)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(101,127)(102,126)(103,130)(104,129)(105,128)(106,147)(107,146)
(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)(115,143)
(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)(123,135)
(124,134)(125,133)(151,227)(152,226)(153,230)(154,229)(155,228)(156,247)
(157,246)(158,250)(159,249)(160,248)(161,242)(162,241)(163,245)(164,244)
(165,243)(166,237)(167,236)(168,240)(169,239)(170,238)(171,232)(172,231)
(173,235)(174,234)(175,233)(176,277)(177,276)(178,280)(179,279)(180,278)
(181,297)(182,296)(183,300)(184,299)(185,298)(186,292)(187,291)(188,295)
(189,294)(190,293)(191,287)(192,286)(193,290)(194,289)(195,288)(196,282)
(197,281)(198,285)(199,284)(200,283)(201,252)(202,251)(203,255)(204,254)
(205,253)(206,272)(207,271)(208,275)(209,274)(210,273)(211,267)(212,266)
(213,270)(214,269)(215,268)(216,262)(217,261)(218,265)(219,264)(220,263)
(221,257)(222,256)(223,260)(224,259)(225,258);;
s2 := ( 1,181)( 2,182)( 3,183)( 4,184)( 5,185)( 6,176)( 7,177)( 8,178)
( 9,179)( 10,180)( 11,196)( 12,197)( 13,198)( 14,199)( 15,200)( 16,191)
( 17,192)( 18,193)( 19,194)( 20,195)( 21,186)( 22,187)( 23,188)( 24,189)
( 25,190)( 26,156)( 27,157)( 28,158)( 29,159)( 30,160)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,171)( 37,172)( 38,173)( 39,174)( 40,175)
( 41,166)( 42,167)( 43,168)( 44,169)( 45,170)( 46,161)( 47,162)( 48,163)
( 49,164)( 50,165)( 51,206)( 52,207)( 53,208)( 54,209)( 55,210)( 56,201)
( 57,202)( 58,203)( 59,204)( 60,205)( 61,221)( 62,222)( 63,223)( 64,224)
( 65,225)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,211)( 72,212)
( 73,213)( 74,214)( 75,215)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,271)( 87,272)( 88,273)
( 89,274)( 90,275)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,261)
( 97,262)( 98,263)( 99,264)(100,265)(101,231)(102,232)(103,233)(104,234)
(105,235)(106,226)(107,227)(108,228)(109,229)(110,230)(111,246)(112,247)
(113,248)(114,249)(115,250)(116,241)(117,242)(118,243)(119,244)(120,245)
(121,236)(122,237)(123,238)(124,239)(125,240)(126,281)(127,282)(128,283)
(129,284)(130,285)(131,276)(132,277)(133,278)(134,279)(135,280)(136,296)
(137,297)(138,298)(139,299)(140,300)(141,291)(142,292)(143,293)(144,294)
(145,295)(146,286)(147,287)(148,288)(149,289)(150,290);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(300)!( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 52)( 27, 51)( 28, 55)
( 29, 54)( 30, 53)( 31, 72)( 32, 71)( 33, 75)( 34, 74)( 35, 73)( 36, 67)
( 37, 66)( 38, 70)( 39, 69)( 40, 68)( 41, 62)( 42, 61)( 43, 65)( 44, 64)
( 45, 63)( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 76, 77)( 78, 80)
( 81, 97)( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)
( 89, 94)( 90, 93)(101,127)(102,126)(103,130)(104,129)(105,128)(106,147)
(107,146)(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)
(115,143)(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)
(123,135)(124,134)(125,133)(151,227)(152,226)(153,230)(154,229)(155,228)
(156,247)(157,246)(158,250)(159,249)(160,248)(161,242)(162,241)(163,245)
(164,244)(165,243)(166,237)(167,236)(168,240)(169,239)(170,238)(171,232)
(172,231)(173,235)(174,234)(175,233)(176,277)(177,276)(178,280)(179,279)
(180,278)(181,297)(182,296)(183,300)(184,299)(185,298)(186,292)(187,291)
(188,295)(189,294)(190,293)(191,287)(192,286)(193,290)(194,289)(195,288)
(196,282)(197,281)(198,285)(199,284)(200,283)(201,252)(202,251)(203,255)
(204,254)(205,253)(206,272)(207,271)(208,275)(209,274)(210,273)(211,267)
(212,266)(213,270)(214,269)(215,268)(216,262)(217,261)(218,265)(219,264)
(220,263)(221,257)(222,256)(223,260)(224,259)(225,258);
s2 := Sym(300)!( 1,181)( 2,182)( 3,183)( 4,184)( 5,185)( 6,176)( 7,177)
( 8,178)( 9,179)( 10,180)( 11,196)( 12,197)( 13,198)( 14,199)( 15,200)
( 16,191)( 17,192)( 18,193)( 19,194)( 20,195)( 21,186)( 22,187)( 23,188)
( 24,189)( 25,190)( 26,156)( 27,157)( 28,158)( 29,159)( 30,160)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,171)( 37,172)( 38,173)( 39,174)
( 40,175)( 41,166)( 42,167)( 43,168)( 44,169)( 45,170)( 46,161)( 47,162)
( 48,163)( 49,164)( 50,165)( 51,206)( 52,207)( 53,208)( 54,209)( 55,210)
( 56,201)( 57,202)( 58,203)( 59,204)( 60,205)( 61,221)( 62,222)( 63,223)
( 64,224)( 65,225)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,211)
( 72,212)( 73,213)( 74,214)( 75,215)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,251)( 82,252)( 83,253)( 84,254)( 85,255)( 86,271)( 87,272)
( 88,273)( 89,274)( 90,275)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)
( 96,261)( 97,262)( 98,263)( 99,264)(100,265)(101,231)(102,232)(103,233)
(104,234)(105,235)(106,226)(107,227)(108,228)(109,229)(110,230)(111,246)
(112,247)(113,248)(114,249)(115,250)(116,241)(117,242)(118,243)(119,244)
(120,245)(121,236)(122,237)(123,238)(124,239)(125,240)(126,281)(127,282)
(128,283)(129,284)(130,285)(131,276)(132,277)(133,278)(134,279)(135,280)
(136,296)(137,297)(138,298)(139,299)(140,300)(141,291)(142,292)(143,293)
(144,294)(145,295)(146,286)(147,287)(148,288)(149,289)(150,290);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope