Polytope of Type {22,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,38}*1672
Also Known As : {22,38|2}. if this polytope has another name.
Group : SmallGroup(1672,30)
Rank : 3
Schlafli Type : {22,38}
Number of vertices, edges, etc : 22, 418, 38
Order of s₀s₁s₂ : 418
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) :
   11-fold quotients : {2,38}*152
   19-fold quotients : {22,2}*88
   22-fold quotients : {2,19}*76
   38-fold quotients : {11,2}*44
   209-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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