Polytope of Type {126,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {126,6}*1512a
Also Known As : {126,6|2}. if this polytope has another name.
Group : SmallGroup(1512,559)
Rank : 3
Schlafli Type : {126,6}
Number of vertices, edges, etc : 126, 378, 6
Order of s0s1s2 : 126
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) :
3-fold quotients : {126,2}*504, {42,6}*504b
6-fold quotients : {63,2}*252
7-fold quotients : {18,6}*216a
9-fold quotients : {14,6}*168, {42,2}*168
18-fold quotients : {21,2}*84
21-fold quotients : {18,2}*72, {6,6}*72a
27-fold quotients : {14,2}*56
42-fold quotients : {9,2}*36
54-fold quotients : {7,2}*28
63-fold quotients : {2,6}*24, {6,2}*24
126-fold quotients : {2,3}*12, {3,2}*12
189-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 19)( 5, 21)( 6, 20)( 7, 16)( 8, 18)( 9, 17)( 10, 13)
( 11, 15)( 12, 14)( 22, 44)( 23, 43)( 24, 45)( 25, 62)( 26, 61)( 27, 63)
( 28, 59)( 29, 58)( 30, 60)( 31, 56)( 32, 55)( 33, 57)( 34, 53)( 35, 52)
( 36, 54)( 37, 50)( 38, 49)( 39, 51)( 40, 47)( 41, 46)( 42, 48)( 65, 66)
( 67, 82)( 68, 84)( 69, 83)( 70, 79)( 71, 81)( 72, 80)( 73, 76)( 74, 78)
( 75, 77)( 85,107)( 86,106)( 87,108)( 88,125)( 89,124)( 90,126)( 91,122)
( 92,121)( 93,123)( 94,119)( 95,118)( 96,120)( 97,116)( 98,115)( 99,117)
(100,113)(101,112)(102,114)(103,110)(104,109)(105,111)(128,129)(130,145)
(131,147)(132,146)(133,142)(134,144)(135,143)(136,139)(137,141)(138,140)
(148,170)(149,169)(150,171)(151,188)(152,187)(153,189)(154,185)(155,184)
(156,186)(157,182)(158,181)(159,183)(160,179)(161,178)(162,180)(163,176)
(164,175)(165,177)(166,173)(167,172)(168,174)(191,192)(193,208)(194,210)
(195,209)(196,205)(197,207)(198,206)(199,202)(200,204)(201,203)(211,233)
(212,232)(213,234)(214,251)(215,250)(216,252)(217,248)(218,247)(219,249)
(220,245)(221,244)(222,246)(223,242)(224,241)(225,243)(226,239)(227,238)
(228,240)(229,236)(230,235)(231,237)(254,255)(256,271)(257,273)(258,272)
(259,268)(260,270)(261,269)(262,265)(263,267)(264,266)(274,296)(275,295)
(276,297)(277,314)(278,313)(279,315)(280,311)(281,310)(282,312)(283,308)
(284,307)(285,309)(286,305)(287,304)(288,306)(289,302)(290,301)(291,303)
(292,299)(293,298)(294,300)(317,318)(319,334)(320,336)(321,335)(322,331)
(323,333)(324,332)(325,328)(326,330)(327,329)(337,359)(338,358)(339,360)
(340,377)(341,376)(342,378)(343,374)(344,373)(345,375)(346,371)(347,370)
(348,372)(349,368)(350,367)(351,369)(352,365)(353,364)(354,366)(355,362)
(356,361)(357,363);;
s1 := ( 1, 25)( 2, 27)( 3, 26)( 4, 22)( 5, 24)( 6, 23)( 7, 40)( 8, 42)
( 9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)( 16, 31)
( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 47)( 44, 46)( 45, 48)
( 49, 62)( 50, 61)( 51, 63)( 52, 59)( 53, 58)( 54, 60)( 55, 56)( 64,151)
( 65,153)( 66,152)( 67,148)( 68,150)( 69,149)( 70,166)( 71,168)( 72,167)
( 73,163)( 74,165)( 75,164)( 76,160)( 77,162)( 78,161)( 79,157)( 80,159)
( 81,158)( 82,154)( 83,156)( 84,155)( 85,130)( 86,132)( 87,131)( 88,127)
( 89,129)( 90,128)( 91,145)( 92,147)( 93,146)( 94,142)( 95,144)( 96,143)
( 97,139)( 98,141)( 99,140)(100,136)(101,138)(102,137)(103,133)(104,135)
(105,134)(106,173)(107,172)(108,174)(109,170)(110,169)(111,171)(112,188)
(113,187)(114,189)(115,185)(116,184)(117,186)(118,182)(119,181)(120,183)
(121,179)(122,178)(123,180)(124,176)(125,175)(126,177)(190,214)(191,216)
(192,215)(193,211)(194,213)(195,212)(196,229)(197,231)(198,230)(199,226)
(200,228)(201,227)(202,223)(203,225)(204,224)(205,220)(206,222)(207,221)
(208,217)(209,219)(210,218)(232,236)(233,235)(234,237)(238,251)(239,250)
(240,252)(241,248)(242,247)(243,249)(244,245)(253,340)(254,342)(255,341)
(256,337)(257,339)(258,338)(259,355)(260,357)(261,356)(262,352)(263,354)
(264,353)(265,349)(266,351)(267,350)(268,346)(269,348)(270,347)(271,343)
(272,345)(273,344)(274,319)(275,321)(276,320)(277,316)(278,318)(279,317)
(280,334)(281,336)(282,335)(283,331)(284,333)(285,332)(286,328)(287,330)
(288,329)(289,325)(290,327)(291,326)(292,322)(293,324)(294,323)(295,362)
(296,361)(297,363)(298,359)(299,358)(300,360)(301,377)(302,376)(303,378)
(304,374)(305,373)(306,375)(307,371)(308,370)(309,372)(310,368)(311,367)
(312,369)(313,365)(314,364)(315,366);;
s2 := ( 1,253)( 2,254)( 3,255)( 4,256)( 5,257)( 6,258)( 7,259)( 8,260)
( 9,261)( 10,262)( 11,263)( 12,264)( 13,265)( 14,266)( 15,267)( 16,268)
( 17,269)( 18,270)( 19,271)( 20,272)( 21,273)( 22,274)( 23,275)( 24,276)
( 25,277)( 26,278)( 27,279)( 28,280)( 29,281)( 30,282)( 31,283)( 32,284)
( 33,285)( 34,286)( 35,287)( 36,288)( 37,289)( 38,290)( 39,291)( 40,292)
( 41,293)( 42,294)( 43,295)( 44,296)( 45,297)( 46,298)( 47,299)( 48,300)
( 49,301)( 50,302)( 51,303)( 52,304)( 53,305)( 54,306)( 55,307)( 56,308)
( 57,309)( 58,310)( 59,311)( 60,312)( 61,313)( 62,314)( 63,315)( 64,190)
( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,197)( 72,198)
( 73,199)( 74,200)( 75,201)( 76,202)( 77,203)( 78,204)( 79,205)( 80,206)
( 81,207)( 82,208)( 83,209)( 84,210)( 85,211)( 86,212)( 87,213)( 88,214)
( 89,215)( 90,216)( 91,217)( 92,218)( 93,219)( 94,220)( 95,221)( 96,222)
( 97,223)( 98,224)( 99,225)(100,226)(101,227)(102,228)(103,229)(104,230)
(105,231)(106,232)(107,233)(108,234)(109,235)(110,236)(111,237)(112,238)
(113,239)(114,240)(115,241)(116,242)(117,243)(118,244)(119,245)(120,246)
(121,247)(122,248)(123,249)(124,250)(125,251)(126,252)(127,316)(128,317)
(129,318)(130,319)(131,320)(132,321)(133,322)(134,323)(135,324)(136,325)
(137,326)(138,327)(139,328)(140,329)(141,330)(142,331)(143,332)(144,333)
(145,334)(146,335)(147,336)(148,337)(149,338)(150,339)(151,340)(152,341)
(153,342)(154,343)(155,344)(156,345)(157,346)(158,347)(159,348)(160,349)
(161,350)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)(168,357)
(169,358)(170,359)(171,360)(172,361)(173,362)(174,363)(175,364)(176,365)
(177,366)(178,367)(179,368)(180,369)(181,370)(182,371)(183,372)(184,373)
(185,374)(186,375)(187,376)(188,377)(189,378);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(378)!( 2, 3)( 4, 19)( 5, 21)( 6, 20)( 7, 16)( 8, 18)( 9, 17)
( 10, 13)( 11, 15)( 12, 14)( 22, 44)( 23, 43)( 24, 45)( 25, 62)( 26, 61)
( 27, 63)( 28, 59)( 29, 58)( 30, 60)( 31, 56)( 32, 55)( 33, 57)( 34, 53)
( 35, 52)( 36, 54)( 37, 50)( 38, 49)( 39, 51)( 40, 47)( 41, 46)( 42, 48)
( 65, 66)( 67, 82)( 68, 84)( 69, 83)( 70, 79)( 71, 81)( 72, 80)( 73, 76)
( 74, 78)( 75, 77)( 85,107)( 86,106)( 87,108)( 88,125)( 89,124)( 90,126)
( 91,122)( 92,121)( 93,123)( 94,119)( 95,118)( 96,120)( 97,116)( 98,115)
( 99,117)(100,113)(101,112)(102,114)(103,110)(104,109)(105,111)(128,129)
(130,145)(131,147)(132,146)(133,142)(134,144)(135,143)(136,139)(137,141)
(138,140)(148,170)(149,169)(150,171)(151,188)(152,187)(153,189)(154,185)
(155,184)(156,186)(157,182)(158,181)(159,183)(160,179)(161,178)(162,180)
(163,176)(164,175)(165,177)(166,173)(167,172)(168,174)(191,192)(193,208)
(194,210)(195,209)(196,205)(197,207)(198,206)(199,202)(200,204)(201,203)
(211,233)(212,232)(213,234)(214,251)(215,250)(216,252)(217,248)(218,247)
(219,249)(220,245)(221,244)(222,246)(223,242)(224,241)(225,243)(226,239)
(227,238)(228,240)(229,236)(230,235)(231,237)(254,255)(256,271)(257,273)
(258,272)(259,268)(260,270)(261,269)(262,265)(263,267)(264,266)(274,296)
(275,295)(276,297)(277,314)(278,313)(279,315)(280,311)(281,310)(282,312)
(283,308)(284,307)(285,309)(286,305)(287,304)(288,306)(289,302)(290,301)
(291,303)(292,299)(293,298)(294,300)(317,318)(319,334)(320,336)(321,335)
(322,331)(323,333)(324,332)(325,328)(326,330)(327,329)(337,359)(338,358)
(339,360)(340,377)(341,376)(342,378)(343,374)(344,373)(345,375)(346,371)
(347,370)(348,372)(349,368)(350,367)(351,369)(352,365)(353,364)(354,366)
(355,362)(356,361)(357,363);
s1 := Sym(378)!( 1, 25)( 2, 27)( 3, 26)( 4, 22)( 5, 24)( 6, 23)( 7, 40)
( 8, 42)( 9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)
( 16, 31)( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 47)( 44, 46)
( 45, 48)( 49, 62)( 50, 61)( 51, 63)( 52, 59)( 53, 58)( 54, 60)( 55, 56)
( 64,151)( 65,153)( 66,152)( 67,148)( 68,150)( 69,149)( 70,166)( 71,168)
( 72,167)( 73,163)( 74,165)( 75,164)( 76,160)( 77,162)( 78,161)( 79,157)
( 80,159)( 81,158)( 82,154)( 83,156)( 84,155)( 85,130)( 86,132)( 87,131)
( 88,127)( 89,129)( 90,128)( 91,145)( 92,147)( 93,146)( 94,142)( 95,144)
( 96,143)( 97,139)( 98,141)( 99,140)(100,136)(101,138)(102,137)(103,133)
(104,135)(105,134)(106,173)(107,172)(108,174)(109,170)(110,169)(111,171)
(112,188)(113,187)(114,189)(115,185)(116,184)(117,186)(118,182)(119,181)
(120,183)(121,179)(122,178)(123,180)(124,176)(125,175)(126,177)(190,214)
(191,216)(192,215)(193,211)(194,213)(195,212)(196,229)(197,231)(198,230)
(199,226)(200,228)(201,227)(202,223)(203,225)(204,224)(205,220)(206,222)
(207,221)(208,217)(209,219)(210,218)(232,236)(233,235)(234,237)(238,251)
(239,250)(240,252)(241,248)(242,247)(243,249)(244,245)(253,340)(254,342)
(255,341)(256,337)(257,339)(258,338)(259,355)(260,357)(261,356)(262,352)
(263,354)(264,353)(265,349)(266,351)(267,350)(268,346)(269,348)(270,347)
(271,343)(272,345)(273,344)(274,319)(275,321)(276,320)(277,316)(278,318)
(279,317)(280,334)(281,336)(282,335)(283,331)(284,333)(285,332)(286,328)
(287,330)(288,329)(289,325)(290,327)(291,326)(292,322)(293,324)(294,323)
(295,362)(296,361)(297,363)(298,359)(299,358)(300,360)(301,377)(302,376)
(303,378)(304,374)(305,373)(306,375)(307,371)(308,370)(309,372)(310,368)
(311,367)(312,369)(313,365)(314,364)(315,366);
s2 := Sym(378)!( 1,253)( 2,254)( 3,255)( 4,256)( 5,257)( 6,258)( 7,259)
( 8,260)( 9,261)( 10,262)( 11,263)( 12,264)( 13,265)( 14,266)( 15,267)
( 16,268)( 17,269)( 18,270)( 19,271)( 20,272)( 21,273)( 22,274)( 23,275)
( 24,276)( 25,277)( 26,278)( 27,279)( 28,280)( 29,281)( 30,282)( 31,283)
( 32,284)( 33,285)( 34,286)( 35,287)( 36,288)( 37,289)( 38,290)( 39,291)
( 40,292)( 41,293)( 42,294)( 43,295)( 44,296)( 45,297)( 46,298)( 47,299)
( 48,300)( 49,301)( 50,302)( 51,303)( 52,304)( 53,305)( 54,306)( 55,307)
( 56,308)( 57,309)( 58,310)( 59,311)( 60,312)( 61,313)( 62,314)( 63,315)
( 64,190)( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,197)
( 72,198)( 73,199)( 74,200)( 75,201)( 76,202)( 77,203)( 78,204)( 79,205)
( 80,206)( 81,207)( 82,208)( 83,209)( 84,210)( 85,211)( 86,212)( 87,213)
( 88,214)( 89,215)( 90,216)( 91,217)( 92,218)( 93,219)( 94,220)( 95,221)
( 96,222)( 97,223)( 98,224)( 99,225)(100,226)(101,227)(102,228)(103,229)
(104,230)(105,231)(106,232)(107,233)(108,234)(109,235)(110,236)(111,237)
(112,238)(113,239)(114,240)(115,241)(116,242)(117,243)(118,244)(119,245)
(120,246)(121,247)(122,248)(123,249)(124,250)(125,251)(126,252)(127,316)
(128,317)(129,318)(130,319)(131,320)(132,321)(133,322)(134,323)(135,324)
(136,325)(137,326)(138,327)(139,328)(140,329)(141,330)(142,331)(143,332)
(144,333)(145,334)(146,335)(147,336)(148,337)(149,338)(150,339)(151,340)
(152,341)(153,342)(154,343)(155,344)(156,345)(157,346)(158,347)(159,348)
(160,349)(161,350)(162,351)(163,352)(164,353)(165,354)(166,355)(167,356)
(168,357)(169,358)(170,359)(171,360)(172,361)(173,362)(174,363)(175,364)
(176,365)(177,366)(178,367)(179,368)(180,369)(181,370)(182,371)(183,372)
(184,373)(185,374)(186,375)(187,376)(188,377)(189,378);
poly := sub<Sym(378)|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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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