Polytope of Type {12,62}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,62}*1488
Also Known As : {12,62|2}. if this polytope has another name.
Group : SmallGroup(1488,147)
Rank : 3
Schlafli Type : {12,62}
Number of vertices, edges, etc : 12, 372, 62
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 : {6,62}*744
3-fold quotients : {4,62}*496
6-fold quotients : {2,62}*248
12-fold quotients : {2,31}*124
31-fold quotients : {12,2}*48
62-fold quotients : {6,2}*24
93-fold quotients : {4,2}*16
124-fold quotients : {3,2}*12
186-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 32, 63)( 33, 64)( 34, 65)( 35, 66)( 36, 67)( 37, 68)( 38, 69)( 39, 70)
( 40, 71)( 41, 72)( 42, 73)( 43, 74)( 44, 75)( 45, 76)( 46, 77)( 47, 78)
( 48, 79)( 49, 80)( 50, 81)( 51, 82)( 52, 83)( 53, 84)( 54, 85)( 55, 86)
( 56, 87)( 57, 88)( 58, 89)( 59, 90)( 60, 91)( 61, 92)( 62, 93)(125,156)
(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)
(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)
(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)
(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(187,280)(188,281)
(189,282)(190,283)(191,284)(192,285)(193,286)(194,287)(195,288)(196,289)
(197,290)(198,291)(199,292)(200,293)(201,294)(202,295)(203,296)(204,297)
(205,298)(206,299)(207,300)(208,301)(209,302)(210,303)(211,304)(212,305)
(213,306)(214,307)(215,308)(216,309)(217,310)(218,342)(219,343)(220,344)
(221,345)(222,346)(223,347)(224,348)(225,349)(226,350)(227,351)(228,352)
(229,353)(230,354)(231,355)(232,356)(233,357)(234,358)(235,359)(236,360)
(237,361)(238,362)(239,363)(240,364)(241,365)(242,366)(243,367)(244,368)
(245,369)(246,370)(247,371)(248,372)(249,311)(250,312)(251,313)(252,314)
(253,315)(254,316)(255,317)(256,318)(257,319)(258,320)(259,321)(260,322)
(261,323)(262,324)(263,325)(264,326)(265,327)(266,328)(267,329)(268,330)
(269,331)(270,332)(271,333)(272,334)(273,335)(274,336)(275,337)(276,338)
(277,339)(278,340)(279,341);;
s1 := ( 1,218)( 2,248)( 3,247)( 4,246)( 5,245)( 6,244)( 7,243)( 8,242)
( 9,241)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,223)( 28,222)( 29,221)( 30,220)( 31,219)( 32,187)
( 33,217)( 34,216)( 35,215)( 36,214)( 37,213)( 38,212)( 39,211)( 40,210)
( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)( 56,194)
( 57,193)( 58,192)( 59,191)( 60,190)( 61,189)( 62,188)( 63,249)( 64,279)
( 65,278)( 66,277)( 67,276)( 68,275)( 69,274)( 70,273)( 71,272)( 72,271)
( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)( 80,263)
( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,257)( 87,256)( 88,255)
( 89,254)( 90,253)( 91,252)( 92,251)( 93,250)( 94,311)( 95,341)( 96,340)
( 97,339)( 98,338)( 99,337)(100,336)(101,335)(102,334)(103,333)(104,332)
(105,331)(106,330)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)
(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)(120,316)
(121,315)(122,314)(123,313)(124,312)(125,280)(126,310)(127,309)(128,308)
(129,307)(130,306)(131,305)(132,304)(133,303)(134,302)(135,301)(136,300)
(137,299)(138,298)(139,297)(140,296)(141,295)(142,294)(143,293)(144,292)
(145,291)(146,290)(147,289)(148,288)(149,287)(150,286)(151,285)(152,284)
(153,283)(154,282)(155,281)(156,342)(157,372)(158,371)(159,370)(160,369)
(161,368)(162,367)(163,366)(164,365)(165,364)(166,363)(167,362)(168,361)
(169,360)(170,359)(171,358)(172,357)(173,356)(174,355)(175,354)(176,353)
(177,352)(178,351)(179,350)(180,349)(181,348)(182,347)(183,346)(184,345)
(185,344)(186,343);;
s2 := ( 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, 33)
( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)
( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)
( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)
( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 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)(125,126)(127,155)(128,154)(129,153)
(130,152)(131,151)(132,150)(133,149)(134,148)(135,147)(136,146)(137,145)
(138,144)(139,143)(140,142)(156,157)(158,186)(159,185)(160,184)(161,183)
(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,176)(169,175)
(170,174)(171,173)(187,188)(189,217)(190,216)(191,215)(192,214)(193,213)
(194,212)(195,211)(196,210)(197,209)(198,208)(199,207)(200,206)(201,205)
(202,204)(218,219)(220,248)(221,247)(222,246)(223,245)(224,244)(225,243)
(226,242)(227,241)(228,240)(229,239)(230,238)(231,237)(232,236)(233,235)
(249,250)(251,279)(252,278)(253,277)(254,276)(255,275)(256,274)(257,273)
(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)(264,266)(280,281)
(282,310)(283,309)(284,308)(285,307)(286,306)(287,305)(288,304)(289,303)
(290,302)(291,301)(292,300)(293,299)(294,298)(295,297)(311,312)(313,341)
(314,340)(315,339)(316,338)(317,337)(318,336)(319,335)(320,334)(321,333)
(322,332)(323,331)(324,330)(325,329)(326,328)(342,343)(344,372)(345,371)
(346,370)(347,369)(348,368)(349,367)(350,366)(351,365)(352,364)(353,363)
(354,362)(355,361)(356,360)(357,359);;
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*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(372)!( 32, 63)( 33, 64)( 34, 65)( 35, 66)( 36, 67)( 37, 68)( 38, 69)
( 39, 70)( 40, 71)( 41, 72)( 42, 73)( 43, 74)( 44, 75)( 45, 76)( 46, 77)
( 47, 78)( 48, 79)( 49, 80)( 50, 81)( 51, 82)( 52, 83)( 53, 84)( 54, 85)
( 55, 86)( 56, 87)( 57, 88)( 58, 89)( 59, 90)( 60, 91)( 61, 92)( 62, 93)
(125,156)(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)
(133,164)(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)
(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)
(149,180)(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(187,280)
(188,281)(189,282)(190,283)(191,284)(192,285)(193,286)(194,287)(195,288)
(196,289)(197,290)(198,291)(199,292)(200,293)(201,294)(202,295)(203,296)
(204,297)(205,298)(206,299)(207,300)(208,301)(209,302)(210,303)(211,304)
(212,305)(213,306)(214,307)(215,308)(216,309)(217,310)(218,342)(219,343)
(220,344)(221,345)(222,346)(223,347)(224,348)(225,349)(226,350)(227,351)
(228,352)(229,353)(230,354)(231,355)(232,356)(233,357)(234,358)(235,359)
(236,360)(237,361)(238,362)(239,363)(240,364)(241,365)(242,366)(243,367)
(244,368)(245,369)(246,370)(247,371)(248,372)(249,311)(250,312)(251,313)
(252,314)(253,315)(254,316)(255,317)(256,318)(257,319)(258,320)(259,321)
(260,322)(261,323)(262,324)(263,325)(264,326)(265,327)(266,328)(267,329)
(268,330)(269,331)(270,332)(271,333)(272,334)(273,335)(274,336)(275,337)
(276,338)(277,339)(278,340)(279,341);
s1 := Sym(372)!( 1,218)( 2,248)( 3,247)( 4,246)( 5,245)( 6,244)( 7,243)
( 8,242)( 9,241)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,223)( 28,222)( 29,221)( 30,220)( 31,219)
( 32,187)( 33,217)( 34,216)( 35,215)( 36,214)( 37,213)( 38,212)( 39,211)
( 40,210)( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)
( 56,194)( 57,193)( 58,192)( 59,191)( 60,190)( 61,189)( 62,188)( 63,249)
( 64,279)( 65,278)( 66,277)( 67,276)( 68,275)( 69,274)( 70,273)( 71,272)
( 72,271)( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)
( 80,263)( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,257)( 87,256)
( 88,255)( 89,254)( 90,253)( 91,252)( 92,251)( 93,250)( 94,311)( 95,341)
( 96,340)( 97,339)( 98,338)( 99,337)(100,336)(101,335)(102,334)(103,333)
(104,332)(105,331)(106,330)(107,329)(108,328)(109,327)(110,326)(111,325)
(112,324)(113,323)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)
(120,316)(121,315)(122,314)(123,313)(124,312)(125,280)(126,310)(127,309)
(128,308)(129,307)(130,306)(131,305)(132,304)(133,303)(134,302)(135,301)
(136,300)(137,299)(138,298)(139,297)(140,296)(141,295)(142,294)(143,293)
(144,292)(145,291)(146,290)(147,289)(148,288)(149,287)(150,286)(151,285)
(152,284)(153,283)(154,282)(155,281)(156,342)(157,372)(158,371)(159,370)
(160,369)(161,368)(162,367)(163,366)(164,365)(165,364)(166,363)(167,362)
(168,361)(169,360)(170,359)(171,358)(172,357)(173,356)(174,355)(175,354)
(176,353)(177,352)(178,351)(179,350)(180,349)(181,348)(182,347)(183,346)
(184,345)(185,344)(186,343);
s2 := 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, 33)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)
( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)
( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)
( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 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)(125,126)(127,155)(128,154)
(129,153)(130,152)(131,151)(132,150)(133,149)(134,148)(135,147)(136,146)
(137,145)(138,144)(139,143)(140,142)(156,157)(158,186)(159,185)(160,184)
(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,176)
(169,175)(170,174)(171,173)(187,188)(189,217)(190,216)(191,215)(192,214)
(193,213)(194,212)(195,211)(196,210)(197,209)(198,208)(199,207)(200,206)
(201,205)(202,204)(218,219)(220,248)(221,247)(222,246)(223,245)(224,244)
(225,243)(226,242)(227,241)(228,240)(229,239)(230,238)(231,237)(232,236)
(233,235)(249,250)(251,279)(252,278)(253,277)(254,276)(255,275)(256,274)
(257,273)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)(264,266)
(280,281)(282,310)(283,309)(284,308)(285,307)(286,306)(287,305)(288,304)
(289,303)(290,302)(291,301)(292,300)(293,299)(294,298)(295,297)(311,312)
(313,341)(314,340)(315,339)(316,338)(317,337)(318,336)(319,335)(320,334)
(321,333)(322,332)(323,331)(324,330)(325,329)(326,328)(342,343)(344,372)
(345,371)(346,370)(347,369)(348,368)(349,367)(350,366)(351,365)(352,364)
(353,363)(354,362)(355,361)(356,360)(357,359);
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,
s0*s1*s0*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*s1*s2*s1*s2 >;
References : None.
to this polytope