Polytope of Type {38,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,26}*1976
Also Known As : {38,26|2}. if this polytope has another name.
Group : SmallGroup(1976,35)
Rank : 3
Schlafli Type : {38,26}
Number of vertices, edges, etc : 38, 494, 26
Order of s0s1s2 : 494
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) :
13-fold quotients : {38,2}*152
19-fold quotients : {2,26}*104
26-fold quotients : {19,2}*76
38-fold quotients : {2,13}*52
247-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)
(458,475)(459,474)(460,473)(461,472)(462,471)(463,470)(464,469)(465,468)
(466,467)(477,494)(478,493)(479,492)(480,491)(481,490)(482,489)(483,488)
(484,487)(485,486);;
s1 := ( 1, 2)( 3, 19)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)( 9, 13)
( 10, 12)( 20,230)( 21,229)( 22,247)( 23,246)( 24,245)( 25,244)( 26,243)
( 27,242)( 28,241)( 29,240)( 30,239)( 31,238)( 32,237)( 33,236)( 34,235)
( 35,234)( 36,233)( 37,232)( 38,231)( 39,211)( 40,210)( 41,228)( 42,227)
( 43,226)( 44,225)( 45,224)( 46,223)( 47,222)( 48,221)( 49,220)( 50,219)
( 51,218)( 52,217)( 53,216)( 54,215)( 55,214)( 56,213)( 57,212)( 58,192)
( 59,191)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)( 65,204)( 66,203)
( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)( 72,197)( 73,196)( 74,195)
( 75,194)( 76,193)( 77,173)( 78,172)( 79,190)( 80,189)( 81,188)( 82,187)
( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)( 88,181)( 89,180)( 90,179)
( 91,178)( 92,177)( 93,176)( 94,175)( 95,174)( 96,154)( 97,153)( 98,171)
( 99,170)(100,169)(101,168)(102,167)(103,166)(104,165)(105,164)(106,163)
(107,162)(108,161)(109,160)(110,159)(111,158)(112,157)(113,156)(114,155)
(115,135)(116,134)(117,152)(118,151)(119,150)(120,149)(121,148)(122,147)
(123,146)(124,145)(125,144)(126,143)(127,142)(128,141)(129,140)(130,139)
(131,138)(132,137)(133,136)(248,249)(250,266)(251,265)(252,264)(253,263)
(254,262)(255,261)(256,260)(257,259)(267,477)(268,476)(269,494)(270,493)
(271,492)(272,491)(273,490)(274,489)(275,488)(276,487)(277,486)(278,485)
(279,484)(280,483)(281,482)(282,481)(283,480)(284,479)(285,478)(286,458)
(287,457)(288,475)(289,474)(290,473)(291,472)(292,471)(293,470)(294,469)
(295,468)(296,467)(297,466)(298,465)(299,464)(300,463)(301,462)(302,461)
(303,460)(304,459)(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)
(343,401)(344,400)(345,418)(346,417)(347,416)(348,415)(349,414)(350,413)
(351,412)(352,411)(353,410)(354,409)(355,408)(356,407)(357,406)(358,405)
(359,404)(360,403)(361,402)(362,382)(363,381)(364,399)(365,398)(366,397)
(367,396)(368,395)(369,394)(370,393)(371,392)(372,391)(373,390)(374,389)
(375,388)(376,387)(377,386)(378,385)(379,384)(380,383);;
s2 := ( 1,267)( 2,268)( 3,269)( 4,270)( 5,271)( 6,272)( 7,273)( 8,274)
( 9,275)( 10,276)( 11,277)( 12,278)( 13,279)( 14,280)( 15,281)( 16,282)
( 17,283)( 18,284)( 19,285)( 20,248)( 21,249)( 22,250)( 23,251)( 24,252)
( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)( 32,260)
( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,476)( 40,477)
( 41,478)( 42,479)( 43,480)( 44,481)( 45,482)( 46,483)( 47,484)( 48,485)
( 49,486)( 50,487)( 51,488)( 52,489)( 53,490)( 54,491)( 55,492)( 56,493)
( 57,494)( 58,457)( 59,458)( 60,459)( 61,460)( 62,461)( 63,462)( 64,463)
( 65,464)( 66,465)( 67,466)( 68,467)( 69,468)( 70,469)( 71,470)( 72,471)
( 73,472)( 74,473)( 75,474)( 76,475)( 77,438)( 78,439)( 79,440)( 80,441)
( 81,442)( 82,443)( 83,444)( 84,445)( 85,446)( 86,447)( 87,448)( 88,449)
( 89,450)( 90,451)( 91,452)( 92,453)( 93,454)( 94,455)( 95,456)( 96,419)
( 97,420)( 98,421)( 99,422)(100,423)(101,424)(102,425)(103,426)(104,427)
(105,428)(106,429)(107,430)(108,431)(109,432)(110,433)(111,434)(112,435)
(113,436)(114,437)(115,400)(116,401)(117,402)(118,403)(119,404)(120,405)
(121,406)(122,407)(123,408)(124,409)(125,410)(126,411)(127,412)(128,413)
(129,414)(130,415)(131,416)(132,417)(133,418)(134,381)(135,382)(136,383)
(137,384)(138,385)(139,386)(140,387)(141,388)(142,389)(143,390)(144,391)
(145,392)(146,393)(147,394)(148,395)(149,396)(150,397)(151,398)(152,399)
(153,362)(154,363)(155,364)(156,365)(157,366)(158,367)(159,368)(160,369)
(161,370)(162,371)(163,372)(164,373)(165,374)(166,375)(167,376)(168,377)
(169,378)(170,379)(171,380)(172,343)(173,344)(174,345)(175,346)(176,347)
(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)(184,355)
(185,356)(186,357)(187,358)(188,359)(189,360)(190,361)(191,324)(192,325)
(193,326)(194,327)(195,328)(196,329)(197,330)(198,331)(199,332)(200,333)
(201,334)(202,335)(203,336)(204,337)(205,338)(206,339)(207,340)(208,341)
(209,342)(210,305)(211,306)(212,307)(213,308)(214,309)(215,310)(216,311)
(217,312)(218,313)(219,314)(220,315)(221,316)(222,317)(223,318)(224,319)
(225,320)(226,321)(227,322)(228,323)(229,286)(230,287)(231,288)(232,289)
(233,290)(234,291)(235,292)(236,293)(237,294)(238,295)(239,296)(240,297)
(241,298)(242,299)(243,300)(244,301)(245,302)(246,303)(247,304);;
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*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(494)!( 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)(458,475)(459,474)(460,473)(461,472)(462,471)(463,470)(464,469)
(465,468)(466,467)(477,494)(478,493)(479,492)(480,491)(481,490)(482,489)
(483,488)(484,487)(485,486);
s1 := Sym(494)!( 1, 2)( 3, 19)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)
( 9, 13)( 10, 12)( 20,230)( 21,229)( 22,247)( 23,246)( 24,245)( 25,244)
( 26,243)( 27,242)( 28,241)( 29,240)( 30,239)( 31,238)( 32,237)( 33,236)
( 34,235)( 35,234)( 36,233)( 37,232)( 38,231)( 39,211)( 40,210)( 41,228)
( 42,227)( 43,226)( 44,225)( 45,224)( 46,223)( 47,222)( 48,221)( 49,220)
( 50,219)( 51,218)( 52,217)( 53,216)( 54,215)( 55,214)( 56,213)( 57,212)
( 58,192)( 59,191)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)( 65,204)
( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)( 72,197)( 73,196)
( 74,195)( 75,194)( 76,193)( 77,173)( 78,172)( 79,190)( 80,189)( 81,188)
( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)( 88,181)( 89,180)
( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174)( 96,154)( 97,153)
( 98,171)( 99,170)(100,169)(101,168)(102,167)(103,166)(104,165)(105,164)
(106,163)(107,162)(108,161)(109,160)(110,159)(111,158)(112,157)(113,156)
(114,155)(115,135)(116,134)(117,152)(118,151)(119,150)(120,149)(121,148)
(122,147)(123,146)(124,145)(125,144)(126,143)(127,142)(128,141)(129,140)
(130,139)(131,138)(132,137)(133,136)(248,249)(250,266)(251,265)(252,264)
(253,263)(254,262)(255,261)(256,260)(257,259)(267,477)(268,476)(269,494)
(270,493)(271,492)(272,491)(273,490)(274,489)(275,488)(276,487)(277,486)
(278,485)(279,484)(280,483)(281,482)(282,481)(283,480)(284,479)(285,478)
(286,458)(287,457)(288,475)(289,474)(290,473)(291,472)(292,471)(293,470)
(294,469)(295,468)(296,467)(297,466)(298,465)(299,464)(300,463)(301,462)
(302,461)(303,460)(304,459)(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)(343,401)(344,400)(345,418)(346,417)(347,416)(348,415)(349,414)
(350,413)(351,412)(352,411)(353,410)(354,409)(355,408)(356,407)(357,406)
(358,405)(359,404)(360,403)(361,402)(362,382)(363,381)(364,399)(365,398)
(366,397)(367,396)(368,395)(369,394)(370,393)(371,392)(372,391)(373,390)
(374,389)(375,388)(376,387)(377,386)(378,385)(379,384)(380,383);
s2 := Sym(494)!( 1,267)( 2,268)( 3,269)( 4,270)( 5,271)( 6,272)( 7,273)
( 8,274)( 9,275)( 10,276)( 11,277)( 12,278)( 13,279)( 14,280)( 15,281)
( 16,282)( 17,283)( 18,284)( 19,285)( 20,248)( 21,249)( 22,250)( 23,251)
( 24,252)( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)
( 32,260)( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,476)
( 40,477)( 41,478)( 42,479)( 43,480)( 44,481)( 45,482)( 46,483)( 47,484)
( 48,485)( 49,486)( 50,487)( 51,488)( 52,489)( 53,490)( 54,491)( 55,492)
( 56,493)( 57,494)( 58,457)( 59,458)( 60,459)( 61,460)( 62,461)( 63,462)
( 64,463)( 65,464)( 66,465)( 67,466)( 68,467)( 69,468)( 70,469)( 71,470)
( 72,471)( 73,472)( 74,473)( 75,474)( 76,475)( 77,438)( 78,439)( 79,440)
( 80,441)( 81,442)( 82,443)( 83,444)( 84,445)( 85,446)( 86,447)( 87,448)
( 88,449)( 89,450)( 90,451)( 91,452)( 92,453)( 93,454)( 94,455)( 95,456)
( 96,419)( 97,420)( 98,421)( 99,422)(100,423)(101,424)(102,425)(103,426)
(104,427)(105,428)(106,429)(107,430)(108,431)(109,432)(110,433)(111,434)
(112,435)(113,436)(114,437)(115,400)(116,401)(117,402)(118,403)(119,404)
(120,405)(121,406)(122,407)(123,408)(124,409)(125,410)(126,411)(127,412)
(128,413)(129,414)(130,415)(131,416)(132,417)(133,418)(134,381)(135,382)
(136,383)(137,384)(138,385)(139,386)(140,387)(141,388)(142,389)(143,390)
(144,391)(145,392)(146,393)(147,394)(148,395)(149,396)(150,397)(151,398)
(152,399)(153,362)(154,363)(155,364)(156,365)(157,366)(158,367)(159,368)
(160,369)(161,370)(162,371)(163,372)(164,373)(165,374)(166,375)(167,376)
(168,377)(169,378)(170,379)(171,380)(172,343)(173,344)(174,345)(175,346)
(176,347)(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)
(184,355)(185,356)(186,357)(187,358)(188,359)(189,360)(190,361)(191,324)
(192,325)(193,326)(194,327)(195,328)(196,329)(197,330)(198,331)(199,332)
(200,333)(201,334)(202,335)(203,336)(204,337)(205,338)(206,339)(207,340)
(208,341)(209,342)(210,305)(211,306)(212,307)(213,308)(214,309)(215,310)
(216,311)(217,312)(218,313)(219,314)(220,315)(221,316)(222,317)(223,318)
(224,319)(225,320)(226,321)(227,322)(228,323)(229,286)(230,287)(231,288)
(232,289)(233,290)(234,291)(235,292)(236,293)(237,294)(238,295)(239,296)
(240,297)(241,298)(242,299)(243,300)(244,301)(245,302)(246,303)(247,304);
poly := sub<Sym(494)|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*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