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