Polytope of Type {62,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {62,12}*1488
Also Known As : {62,12|2}. if this polytope has another name.
Group : SmallGroup(1488,147)
Rank : 3
Schlafli Type : {62,12}
Number of vertices, edges, etc : 62, 372, 12
Order of s₀s₁s₂ : 372
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 : {62,6}*744
   3-fold quotients : {62,4}*496
   6-fold quotients : {62,2}*248
   12-fold quotients : {31,2}*124
   31-fold quotients : {2,12}*48
   62-fold quotients : {2,6}*24
   93-fold quotients : {2,4}*16
   124-fold quotients : {2,3}*12
   186-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)(  9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 33, 62)
( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)( 41, 54)
( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)( 65, 92)
( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)( 97,122)
( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)
(106,113)(107,112)(108,111)(109,110)(126,155)(127,154)(128,153)(129,152)
(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)
(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)(161,182)
(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)
(170,173)(171,172)(188,217)(189,216)(190,215)(191,214)(192,213)(193,212)
(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)(200,205)(201,204)
(202,203)(219,248)(220,247)(221,246)(222,245)(223,244)(224,243)(225,242)
(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)(232,235)(233,234)
(250,279)(251,278)(252,277)(253,276)(254,275)(255,274)(256,273)(257,272)
(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)(281,310)
(282,309)(283,308)(284,307)(285,306)(286,305)(287,304)(288,303)(289,302)
(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(312,341)(313,340)
(314,339)(315,338)(316,337)(317,336)(318,335)(319,334)(320,333)(321,332)
(322,331)(323,330)(324,329)(325,328)(326,327)(343,372)(344,371)(345,370)
(346,369)(347,368)(348,367)(349,366)(350,365)(351,364)(352,363)(353,362)
(354,361)(355,360)(356,359)(357,358);;
s1 := (  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)
( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 64)
( 33, 63)( 34, 93)( 35, 92)( 36, 91)( 37, 90)( 38, 89)( 39, 88)( 40, 87)
( 41, 86)( 42, 85)( 43, 84)( 44, 83)( 45, 82)( 46, 81)( 47, 80)( 48, 79)
( 49, 78)( 50, 77)( 51, 76)( 52, 75)( 53, 74)( 54, 73)( 55, 72)( 56, 71)
( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 94, 95)( 96,124)
( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)
(105,115)(106,114)(107,113)(108,112)(109,111)(125,157)(126,156)(127,186)
(128,185)(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)(135,178)
(136,177)(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)(143,170)
(144,169)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)
(152,161)(153,160)(154,159)(155,158)(187,281)(188,280)(189,310)(190,309)
(191,308)(192,307)(193,306)(194,305)(195,304)(196,303)(197,302)(198,301)
(199,300)(200,299)(201,298)(202,297)(203,296)(204,295)(205,294)(206,293)
(207,292)(208,291)(209,290)(210,289)(211,288)(212,287)(213,286)(214,285)
(215,284)(216,283)(217,282)(218,343)(219,342)(220,372)(221,371)(222,370)
(223,369)(224,368)(225,367)(226,366)(227,365)(228,364)(229,363)(230,362)
(231,361)(232,360)(233,359)(234,358)(235,357)(236,356)(237,355)(238,354)
(239,353)(240,352)(241,351)(242,350)(243,349)(244,348)(245,347)(246,346)
(247,345)(248,344)(249,312)(250,311)(251,341)(252,340)(253,339)(254,338)
(255,337)(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)
(263,329)(264,328)(265,327)(266,326)(267,325)(268,324)(269,323)(270,322)
(271,321)(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)
(279,313);;
s2 := (  1,218)(  2,219)(  3,220)(  4,221)(  5,222)(  6,223)(  7,224)(  8,225)
(  9,226)( 10,227)( 11,228)( 12,229)( 13,230)( 14,231)( 15,232)( 16,233)
( 17,234)( 18,235)( 19,236)( 20,237)( 21,238)( 22,239)( 23,240)( 24,241)
( 25,242)( 26,243)( 27,244)( 28,245)( 29,246)( 30,247)( 31,248)( 32,187)
( 33,188)( 34,189)( 35,190)( 36,191)( 37,192)( 38,193)( 39,194)( 40,195)
( 41,196)( 42,197)( 43,198)( 44,199)( 45,200)( 46,201)( 47,202)( 48,203)
( 49,204)( 50,205)( 51,206)( 52,207)( 53,208)( 54,209)( 55,210)( 56,211)
( 57,212)( 58,213)( 59,214)( 60,215)( 61,216)( 62,217)( 63,249)( 64,250)
( 65,251)( 66,252)( 67,253)( 68,254)( 69,255)( 70,256)( 71,257)( 72,258)
( 73,259)( 74,260)( 75,261)( 76,262)( 77,263)( 78,264)( 79,265)( 80,266)
( 81,267)( 82,268)( 83,269)( 84,270)( 85,271)( 86,272)( 87,273)( 88,274)
( 89,275)( 90,276)( 91,277)( 92,278)( 93,279)( 94,311)( 95,312)( 96,313)
( 97,314)( 98,315)( 99,316)(100,317)(101,318)(102,319)(103,320)(104,321)
(105,322)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)(112,329)
(113,330)(114,331)(115,332)(116,333)(117,334)(118,335)(119,336)(120,337)
(121,338)(122,339)(123,340)(124,341)(125,280)(126,281)(127,282)(128,283)
(129,284)(130,285)(131,286)(132,287)(133,288)(134,289)(135,290)(136,291)
(137,292)(138,293)(139,294)(140,295)(141,296)(142,297)(143,298)(144,299)
(145,300)(146,301)(147,302)(148,303)(149,304)(150,305)(151,306)(152,307)
(153,308)(154,309)(155,310)(156,342)(157,343)(158,344)(159,345)(160,346)
(161,347)(162,348)(163,349)(164,350)(165,351)(166,352)(167,353)(168,354)
(169,355)(170,356)(171,357)(172,358)(173,359)(174,360)(175,361)(176,362)
(177,363)(178,364)(179,365)(180,366)(181,367)(182,368)(183,369)(184,370)
(185,371)(186,372);;
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*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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(372)!(  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)
(  9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 33, 62)( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)
( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)
( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)
( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)
( 97,122)( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)
(105,114)(106,113)(107,112)(108,111)(109,110)(126,155)(127,154)(128,153)
(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)
(137,144)(138,143)(139,142)(140,141)(157,186)(158,185)(159,184)(160,183)
(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)
(169,174)(170,173)(171,172)(188,217)(189,216)(190,215)(191,214)(192,213)
(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(199,206)(200,205)
(201,204)(202,203)(219,248)(220,247)(221,246)(222,245)(223,244)(224,243)
(225,242)(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)(232,235)
(233,234)(250,279)(251,278)(252,277)(253,276)(254,275)(255,274)(256,273)
(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)
(281,310)(282,309)(283,308)(284,307)(285,306)(286,305)(287,304)(288,303)
(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(312,341)
(313,340)(314,339)(315,338)(316,337)(317,336)(318,335)(319,334)(320,333)
(321,332)(322,331)(323,330)(324,329)(325,328)(326,327)(343,372)(344,371)
(345,370)(346,369)(347,368)(348,367)(349,366)(350,365)(351,364)(352,363)
(353,362)(354,361)(355,360)(356,359)(357,358);
s1 := Sym(372)!(  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)
(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)
( 32, 64)( 33, 63)( 34, 93)( 35, 92)( 36, 91)( 37, 90)( 38, 89)( 39, 88)
( 40, 87)( 41, 86)( 42, 85)( 43, 84)( 44, 83)( 45, 82)( 46, 81)( 47, 80)
( 48, 79)( 49, 78)( 50, 77)( 51, 76)( 52, 75)( 53, 74)( 54, 73)( 55, 72)
( 56, 71)( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 94, 95)
( 96,124)( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)
(104,116)(105,115)(106,114)(107,113)(108,112)(109,111)(125,157)(126,156)
(127,186)(128,185)(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)
(135,178)(136,177)(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)
(143,170)(144,169)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)
(151,162)(152,161)(153,160)(154,159)(155,158)(187,281)(188,280)(189,310)
(190,309)(191,308)(192,307)(193,306)(194,305)(195,304)(196,303)(197,302)
(198,301)(199,300)(200,299)(201,298)(202,297)(203,296)(204,295)(205,294)
(206,293)(207,292)(208,291)(209,290)(210,289)(211,288)(212,287)(213,286)
(214,285)(215,284)(216,283)(217,282)(218,343)(219,342)(220,372)(221,371)
(222,370)(223,369)(224,368)(225,367)(226,366)(227,365)(228,364)(229,363)
(230,362)(231,361)(232,360)(233,359)(234,358)(235,357)(236,356)(237,355)
(238,354)(239,353)(240,352)(241,351)(242,350)(243,349)(244,348)(245,347)
(246,346)(247,345)(248,344)(249,312)(250,311)(251,341)(252,340)(253,339)
(254,338)(255,337)(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)
(262,330)(263,329)(264,328)(265,327)(266,326)(267,325)(268,324)(269,323)
(270,322)(271,321)(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)
(278,314)(279,313);
s2 := Sym(372)!(  1,218)(  2,219)(  3,220)(  4,221)(  5,222)(  6,223)(  7,224)
(  8,225)(  9,226)( 10,227)( 11,228)( 12,229)( 13,230)( 14,231)( 15,232)
( 16,233)( 17,234)( 18,235)( 19,236)( 20,237)( 21,238)( 22,239)( 23,240)
( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,246)( 30,247)( 31,248)
( 32,187)( 33,188)( 34,189)( 35,190)( 36,191)( 37,192)( 38,193)( 39,194)
( 40,195)( 41,196)( 42,197)( 43,198)( 44,199)( 45,200)( 46,201)( 47,202)
( 48,203)( 49,204)( 50,205)( 51,206)( 52,207)( 53,208)( 54,209)( 55,210)
( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 61,216)( 62,217)( 63,249)
( 64,250)( 65,251)( 66,252)( 67,253)( 68,254)( 69,255)( 70,256)( 71,257)
( 72,258)( 73,259)( 74,260)( 75,261)( 76,262)( 77,263)( 78,264)( 79,265)
( 80,266)( 81,267)( 82,268)( 83,269)( 84,270)( 85,271)( 86,272)( 87,273)
( 88,274)( 89,275)( 90,276)( 91,277)( 92,278)( 93,279)( 94,311)( 95,312)
( 96,313)( 97,314)( 98,315)( 99,316)(100,317)(101,318)(102,319)(103,320)
(104,321)(105,322)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)
(112,329)(113,330)(114,331)(115,332)(116,333)(117,334)(118,335)(119,336)
(120,337)(121,338)(122,339)(123,340)(124,341)(125,280)(126,281)(127,282)
(128,283)(129,284)(130,285)(131,286)(132,287)(133,288)(134,289)(135,290)
(136,291)(137,292)(138,293)(139,294)(140,295)(141,296)(142,297)(143,298)
(144,299)(145,300)(146,301)(147,302)(148,303)(149,304)(150,305)(151,306)
(152,307)(153,308)(154,309)(155,310)(156,342)(157,343)(158,344)(159,345)
(160,346)(161,347)(162,348)(163,349)(164,350)(165,351)(166,352)(167,353)
(168,354)(169,355)(170,356)(171,357)(172,358)(173,359)(174,360)(175,361)
(176,362)(177,363)(178,364)(179,365)(180,366)(181,367)(182,368)(183,369)
(184,370)(185,371)(186,372);
poly := sub<Sym(372)|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*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*s0*s1*s0*s1 >;

References : None.
to this polytope