Polytope of Type {38,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,24}*1824
Also Known As : {38,24|2}. if this polytope has another name.
Group : SmallGroup(1824,392)
Rank : 3
Schlafli Type : {38,24}
Number of vertices, edges, etc : 38, 456, 24
Order of s0s1s2 : 456
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 : {38,12}*912
3-fold quotients : {38,8}*608
4-fold quotients : {38,6}*456
6-fold quotients : {38,4}*304
12-fold quotients : {38,2}*152
19-fold quotients : {2,24}*96
24-fold quotients : {19,2}*76
38-fold quotients : {2,12}*48
57-fold quotients : {2,8}*32
76-fold quotients : {2,6}*24
114-fold quotients : {2,4}*16
152-fold quotients : {2,3}*12
228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)( 81, 92)
( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)( 99,112)
(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)(117,132)
(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(135,152)
(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)
(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)
(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)
(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)(215,224)
(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)(233,244)
(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)(251,264)
(252,263)(253,262)(254,261)(255,260)(256,259)(257,258)(268,285)(269,284)
(270,283)(271,282)(272,281)(273,280)(274,279)(275,278)(276,277)(287,304)
(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)
(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)(313,316)
(314,315)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)(331,336)
(332,335)(333,334)(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)
(350,355)(351,354)(352,353)(363,380)(364,379)(365,378)(366,377)(367,376)
(368,375)(369,374)(370,373)(371,372)(382,399)(383,398)(384,397)(385,396)
(386,395)(387,394)(388,393)(389,392)(390,391)(401,418)(402,417)(403,416)
(404,415)(405,414)(406,413)(407,412)(408,411)(409,410)(420,437)(421,436)
(422,435)(423,434)(424,433)(425,432)(426,431)(427,430)(428,429)(439,456)
(440,455)(441,454)(442,453)(443,452)(444,451)(445,450)(446,449)(447,448);;
s1 := ( 1, 2)( 3, 19)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)( 9, 13)
( 10, 12)( 20, 40)( 21, 39)( 22, 57)( 23, 56)( 24, 55)( 25, 54)( 26, 53)
( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 58, 59)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 97)( 78, 96)( 79,114)
( 80,113)( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)
( 88,105)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)
(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)(122,185)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)(130,177)
(131,176)(132,175)(133,174)(134,211)(135,210)(136,228)(137,227)(138,226)
(139,225)(140,224)(141,223)(142,222)(143,221)(144,220)(145,219)(146,218)
(147,217)(148,216)(149,215)(150,214)(151,213)(152,212)(153,192)(154,191)
(155,209)(156,208)(157,207)(158,206)(159,205)(160,204)(161,203)(162,202)
(163,201)(164,200)(165,199)(166,198)(167,197)(168,196)(169,195)(170,194)
(171,193)(229,344)(230,343)(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)(248,382)(249,381)(250,399)(251,398)
(252,397)(253,396)(254,395)(255,394)(256,393)(257,392)(258,391)(259,390)
(260,389)(261,388)(262,387)(263,386)(264,385)(265,384)(266,383)(267,363)
(268,362)(269,380)(270,379)(271,378)(272,377)(273,376)(274,375)(275,374)
(276,373)(277,372)(278,371)(279,370)(280,369)(281,368)(282,367)(283,366)
(284,365)(285,364)(286,401)(287,400)(288,418)(289,417)(290,416)(291,415)
(292,414)(293,413)(294,412)(295,411)(296,410)(297,409)(298,408)(299,407)
(300,406)(301,405)(302,404)(303,403)(304,402)(305,439)(306,438)(307,456)
(308,455)(309,454)(310,453)(311,452)(312,451)(313,450)(314,449)(315,448)
(316,447)(317,446)(318,445)(319,444)(320,443)(321,442)(322,441)(323,440)
(324,420)(325,419)(326,437)(327,436)(328,435)(329,434)(330,433)(331,432)
(332,431)(333,430)(334,429)(335,428)(336,427)(337,426)(338,425)(339,424)
(340,423)(341,422)(342,421);;
s2 := ( 1,248)( 2,249)( 3,250)( 4,251)( 5,252)( 6,253)( 7,254)( 8,255)
( 9,256)( 10,257)( 11,258)( 12,259)( 13,260)( 14,261)( 15,262)( 16,263)
( 17,264)( 18,265)( 19,266)( 20,229)( 21,230)( 22,231)( 23,232)( 24,233)
( 25,234)( 26,235)( 27,236)( 28,237)( 29,238)( 30,239)( 31,240)( 32,241)
( 33,242)( 34,243)( 35,244)( 36,245)( 37,246)( 38,247)( 39,267)( 40,268)
( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)
( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)
( 57,285)( 58,305)( 59,306)( 60,307)( 61,308)( 62,309)( 63,310)( 64,311)
( 65,312)( 66,313)( 67,314)( 68,315)( 69,316)( 70,317)( 71,318)( 72,319)
( 73,320)( 74,321)( 75,322)( 76,323)( 77,286)( 78,287)( 79,288)( 80,289)
( 81,290)( 82,291)( 83,292)( 84,293)( 85,294)( 86,295)( 87,296)( 88,297)
( 89,298)( 90,299)( 91,300)( 92,301)( 93,302)( 94,303)( 95,304)( 96,324)
( 97,325)( 98,326)( 99,327)(100,328)(101,329)(102,330)(103,331)(104,332)
(105,333)(106,334)(107,335)(108,336)(109,337)(110,338)(111,339)(112,340)
(113,341)(114,342)(115,419)(116,420)(117,421)(118,422)(119,423)(120,424)
(121,425)(122,426)(123,427)(124,428)(125,429)(126,430)(127,431)(128,432)
(129,433)(130,434)(131,435)(132,436)(133,437)(134,400)(135,401)(136,402)
(137,403)(138,404)(139,405)(140,406)(141,407)(142,408)(143,409)(144,410)
(145,411)(146,412)(147,413)(148,414)(149,415)(150,416)(151,417)(152,418)
(153,438)(154,439)(155,440)(156,441)(157,442)(158,443)(159,444)(160,445)
(161,446)(162,447)(163,448)(164,449)(165,450)(166,451)(167,452)(168,453)
(169,454)(170,455)(171,456)(172,362)(173,363)(174,364)(175,365)(176,366)
(177,367)(178,368)(179,369)(180,370)(181,371)(182,372)(183,373)(184,374)
(185,375)(186,376)(187,377)(188,378)(189,379)(190,380)(191,343)(192,344)
(193,345)(194,346)(195,347)(196,348)(197,349)(198,350)(199,351)(200,352)
(201,353)(202,354)(203,355)(204,356)(205,357)(206,358)(207,359)(208,360)
(209,361)(210,381)(211,382)(212,383)(213,384)(214,385)(215,386)(216,387)
(217,388)(218,389)(219,390)(220,391)(221,392)(222,393)(223,394)(224,395)
(225,396)(226,397)(227,398)(228,399);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(456)!( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)
( 9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)
( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)
( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)
(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)
(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)
(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164)(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)
(179,184)(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)
(215,224)(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)
(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)
(251,264)(252,263)(253,262)(254,261)(255,260)(256,259)(257,258)(268,285)
(269,284)(270,283)(271,282)(272,281)(273,280)(274,279)(275,278)(276,277)
(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)
(295,296)(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)
(313,316)(314,315)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)
(331,336)(332,335)(333,334)(344,361)(345,360)(346,359)(347,358)(348,357)
(349,356)(350,355)(351,354)(352,353)(363,380)(364,379)(365,378)(366,377)
(367,376)(368,375)(369,374)(370,373)(371,372)(382,399)(383,398)(384,397)
(385,396)(386,395)(387,394)(388,393)(389,392)(390,391)(401,418)(402,417)
(403,416)(404,415)(405,414)(406,413)(407,412)(408,411)(409,410)(420,437)
(421,436)(422,435)(423,434)(424,433)(425,432)(426,431)(427,430)(428,429)
(439,456)(440,455)(441,454)(442,453)(443,452)(444,451)(445,450)(446,449)
(447,448);
s1 := Sym(456)!( 1, 2)( 3, 19)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)
( 9, 13)( 10, 12)( 20, 40)( 21, 39)( 22, 57)( 23, 56)( 24, 55)( 25, 54)
( 26, 53)( 27, 52)( 28, 51)( 29, 50)( 30, 49)( 31, 48)( 32, 47)( 33, 46)
( 34, 45)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 58, 59)( 60, 76)( 61, 75)
( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 77, 97)( 78, 96)
( 79,114)( 80,113)( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)
( 87,106)( 88,105)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)
( 95, 98)(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)
(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)
(130,177)(131,176)(132,175)(133,174)(134,211)(135,210)(136,228)(137,227)
(138,226)(139,225)(140,224)(141,223)(142,222)(143,221)(144,220)(145,219)
(146,218)(147,217)(148,216)(149,215)(150,214)(151,213)(152,212)(153,192)
(154,191)(155,209)(156,208)(157,207)(158,206)(159,205)(160,204)(161,203)
(162,202)(163,201)(164,200)(165,199)(166,198)(167,197)(168,196)(169,195)
(170,194)(171,193)(229,344)(230,343)(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)(248,382)(249,381)(250,399)
(251,398)(252,397)(253,396)(254,395)(255,394)(256,393)(257,392)(258,391)
(259,390)(260,389)(261,388)(262,387)(263,386)(264,385)(265,384)(266,383)
(267,363)(268,362)(269,380)(270,379)(271,378)(272,377)(273,376)(274,375)
(275,374)(276,373)(277,372)(278,371)(279,370)(280,369)(281,368)(282,367)
(283,366)(284,365)(285,364)(286,401)(287,400)(288,418)(289,417)(290,416)
(291,415)(292,414)(293,413)(294,412)(295,411)(296,410)(297,409)(298,408)
(299,407)(300,406)(301,405)(302,404)(303,403)(304,402)(305,439)(306,438)
(307,456)(308,455)(309,454)(310,453)(311,452)(312,451)(313,450)(314,449)
(315,448)(316,447)(317,446)(318,445)(319,444)(320,443)(321,442)(322,441)
(323,440)(324,420)(325,419)(326,437)(327,436)(328,435)(329,434)(330,433)
(331,432)(332,431)(333,430)(334,429)(335,428)(336,427)(337,426)(338,425)
(339,424)(340,423)(341,422)(342,421);
s2 := Sym(456)!( 1,248)( 2,249)( 3,250)( 4,251)( 5,252)( 6,253)( 7,254)
( 8,255)( 9,256)( 10,257)( 11,258)( 12,259)( 13,260)( 14,261)( 15,262)
( 16,263)( 17,264)( 18,265)( 19,266)( 20,229)( 21,230)( 22,231)( 23,232)
( 24,233)( 25,234)( 26,235)( 27,236)( 28,237)( 29,238)( 30,239)( 31,240)
( 32,241)( 33,242)( 34,243)( 35,244)( 36,245)( 37,246)( 38,247)( 39,267)
( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)
( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)
( 56,284)( 57,285)( 58,305)( 59,306)( 60,307)( 61,308)( 62,309)( 63,310)
( 64,311)( 65,312)( 66,313)( 67,314)( 68,315)( 69,316)( 70,317)( 71,318)
( 72,319)( 73,320)( 74,321)( 75,322)( 76,323)( 77,286)( 78,287)( 79,288)
( 80,289)( 81,290)( 82,291)( 83,292)( 84,293)( 85,294)( 86,295)( 87,296)
( 88,297)( 89,298)( 90,299)( 91,300)( 92,301)( 93,302)( 94,303)( 95,304)
( 96,324)( 97,325)( 98,326)( 99,327)(100,328)(101,329)(102,330)(103,331)
(104,332)(105,333)(106,334)(107,335)(108,336)(109,337)(110,338)(111,339)
(112,340)(113,341)(114,342)(115,419)(116,420)(117,421)(118,422)(119,423)
(120,424)(121,425)(122,426)(123,427)(124,428)(125,429)(126,430)(127,431)
(128,432)(129,433)(130,434)(131,435)(132,436)(133,437)(134,400)(135,401)
(136,402)(137,403)(138,404)(139,405)(140,406)(141,407)(142,408)(143,409)
(144,410)(145,411)(146,412)(147,413)(148,414)(149,415)(150,416)(151,417)
(152,418)(153,438)(154,439)(155,440)(156,441)(157,442)(158,443)(159,444)
(160,445)(161,446)(162,447)(163,448)(164,449)(165,450)(166,451)(167,452)
(168,453)(169,454)(170,455)(171,456)(172,362)(173,363)(174,364)(175,365)
(176,366)(177,367)(178,368)(179,369)(180,370)(181,371)(182,372)(183,373)
(184,374)(185,375)(186,376)(187,377)(188,378)(189,379)(190,380)(191,343)
(192,344)(193,345)(194,346)(195,347)(196,348)(197,349)(198,350)(199,351)
(200,352)(201,353)(202,354)(203,355)(204,356)(205,357)(206,358)(207,359)
(208,360)(209,361)(210,381)(211,382)(212,383)(213,384)(214,385)(215,386)
(216,387)(217,388)(218,389)(219,390)(220,391)(221,392)(222,393)(223,394)
(224,395)(225,396)(226,397)(227,398)(228,399);
poly := sub<Sym(456)|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*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 >;
References : None.
to this polytope