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