Polytope of Type {38,22}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,22}*1672
Also Known As : {38,22|2}. if this polytope has another name.
Group : SmallGroup(1672,30)
Rank : 3
Schlafli Type : {38,22}
Number of vertices, edges, etc : 38, 418, 22
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 : {38,2}*152
19-fold quotients : {2,22}*88
22-fold quotients : {19,2}*76
38-fold quotients : {2,11}*44
209-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);;
s1 := ( 1, 2)( 3, 19)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)( 9, 13)
( 10, 12)( 20,192)( 21,191)( 22,209)( 23,208)( 24,207)( 25,206)( 26,205)
( 27,204)( 28,203)( 29,202)( 30,201)( 31,200)( 32,199)( 33,198)( 34,197)
( 35,196)( 36,195)( 37,194)( 38,193)( 39,173)( 40,172)( 41,190)( 42,189)
( 43,188)( 44,187)( 45,186)( 46,185)( 47,184)( 48,183)( 49,182)( 50,181)
( 51,180)( 52,179)( 53,178)( 54,177)( 55,176)( 56,175)( 57,174)( 58,154)
( 59,153)( 60,171)( 61,170)( 62,169)( 63,168)( 64,167)( 65,166)( 66,165)
( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)( 73,158)( 74,157)
( 75,156)( 76,155)( 77,135)( 78,134)( 79,152)( 80,151)( 81,150)( 82,149)
( 83,148)( 84,147)( 85,146)( 86,145)( 87,144)( 88,143)( 89,142)( 90,141)
( 91,140)( 92,139)( 93,138)( 94,137)( 95,136)( 96,116)( 97,115)( 98,133)
( 99,132)(100,131)(101,130)(102,129)(103,128)(104,127)(105,126)(106,125)
(107,124)(108,123)(109,122)(110,121)(111,120)(112,119)(113,118)(114,117)
(210,211)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)
(219,221)(229,401)(230,400)(231,418)(232,417)(233,416)(234,415)(235,414)
(236,413)(237,412)(238,411)(239,410)(240,409)(241,408)(242,407)(243,406)
(244,405)(245,404)(246,403)(247,402)(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)(286,344)(287,343)(288,361)(289,360)(290,359)(291,358)
(292,357)(293,356)(294,355)(295,354)(296,353)(297,352)(298,351)(299,350)
(300,349)(301,348)(302,347)(303,346)(304,345)(305,325)(306,324)(307,342)
(308,341)(309,340)(310,339)(311,338)(312,337)(313,336)(314,335)(315,334)
(316,333)(317,332)(318,331)(319,330)(320,329)(321,328)(322,327)(323,326);;
s2 := ( 1,229)( 2,230)( 3,231)( 4,232)( 5,233)( 6,234)( 7,235)( 8,236)
( 9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)( 16,244)
( 17,245)( 18,246)( 19,247)( 20,210)( 21,211)( 22,212)( 23,213)( 24,214)
( 25,215)( 26,216)( 27,217)( 28,218)( 29,219)( 30,220)( 31,221)( 32,222)
( 33,223)( 34,224)( 35,225)( 36,226)( 37,227)( 38,228)( 39,400)( 40,401)
( 41,402)( 42,403)( 43,404)( 44,405)( 45,406)( 46,407)( 47,408)( 48,409)
( 49,410)( 50,411)( 51,412)( 52,413)( 53,414)( 54,415)( 55,416)( 56,417)
( 57,418)( 58,381)( 59,382)( 60,383)( 61,384)( 62,385)( 63,386)( 64,387)
( 65,388)( 66,389)( 67,390)( 68,391)( 69,392)( 70,393)( 71,394)( 72,395)
( 73,396)( 74,397)( 75,398)( 76,399)( 77,362)( 78,363)( 79,364)( 80,365)
( 81,366)( 82,367)( 83,368)( 84,369)( 85,370)( 86,371)( 87,372)( 88,373)
( 89,374)( 90,375)( 91,376)( 92,377)( 93,378)( 94,379)( 95,380)( 96,343)
( 97,344)( 98,345)( 99,346)(100,347)(101,348)(102,349)(103,350)(104,351)
(105,352)(106,353)(107,354)(108,355)(109,356)(110,357)(111,358)(112,359)
(113,360)(114,361)(115,324)(116,325)(117,326)(118,327)(119,328)(120,329)
(121,330)(122,331)(123,332)(124,333)(125,334)(126,335)(127,336)(128,337)
(129,338)(130,339)(131,340)(132,341)(133,342)(134,305)(135,306)(136,307)
(137,308)(138,309)(139,310)(140,311)(141,312)(142,313)(143,314)(144,315)
(145,316)(146,317)(147,318)(148,319)(149,320)(150,321)(151,322)(152,323)
(153,286)(154,287)(155,288)(156,289)(157,290)(158,291)(159,292)(160,293)
(161,294)(162,295)(163,296)(164,297)(165,298)(166,299)(167,300)(168,301)
(169,302)(170,303)(171,304)(172,267)(173,268)(174,269)(175,270)(176,271)
(177,272)(178,273)(179,274)(180,275)(181,276)(182,277)(183,278)(184,279)
(185,280)(186,281)(187,282)(188,283)(189,284)(190,285)(191,248)(192,249)
(193,250)(194,251)(195,252)(196,253)(197,254)(198,255)(199,256)(200,257)
(201,258)(202,259)(203,260)(204,261)(205,262)(206,263)(207,264)(208,265)
(209,266);;
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,
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(418)!( 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);
s1 := Sym(418)!( 1, 2)( 3, 19)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)
( 9, 13)( 10, 12)( 20,192)( 21,191)( 22,209)( 23,208)( 24,207)( 25,206)
( 26,205)( 27,204)( 28,203)( 29,202)( 30,201)( 31,200)( 32,199)( 33,198)
( 34,197)( 35,196)( 36,195)( 37,194)( 38,193)( 39,173)( 40,172)( 41,190)
( 42,189)( 43,188)( 44,187)( 45,186)( 46,185)( 47,184)( 48,183)( 49,182)
( 50,181)( 51,180)( 52,179)( 53,178)( 54,177)( 55,176)( 56,175)( 57,174)
( 58,154)( 59,153)( 60,171)( 61,170)( 62,169)( 63,168)( 64,167)( 65,166)
( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)( 73,158)
( 74,157)( 75,156)( 76,155)( 77,135)( 78,134)( 79,152)( 80,151)( 81,150)
( 82,149)( 83,148)( 84,147)( 85,146)( 86,145)( 87,144)( 88,143)( 89,142)
( 90,141)( 91,140)( 92,139)( 93,138)( 94,137)( 95,136)( 96,116)( 97,115)
( 98,133)( 99,132)(100,131)(101,130)(102,129)(103,128)(104,127)(105,126)
(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)(112,119)(113,118)
(114,117)(210,211)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)
(218,222)(219,221)(229,401)(230,400)(231,418)(232,417)(233,416)(234,415)
(235,414)(236,413)(237,412)(238,411)(239,410)(240,409)(241,408)(242,407)
(243,406)(244,405)(245,404)(246,403)(247,402)(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)(286,344)(287,343)(288,361)(289,360)(290,359)
(291,358)(292,357)(293,356)(294,355)(295,354)(296,353)(297,352)(298,351)
(299,350)(300,349)(301,348)(302,347)(303,346)(304,345)(305,325)(306,324)
(307,342)(308,341)(309,340)(310,339)(311,338)(312,337)(313,336)(314,335)
(315,334)(316,333)(317,332)(318,331)(319,330)(320,329)(321,328)(322,327)
(323,326);
s2 := Sym(418)!( 1,229)( 2,230)( 3,231)( 4,232)( 5,233)( 6,234)( 7,235)
( 8,236)( 9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)
( 16,244)( 17,245)( 18,246)( 19,247)( 20,210)( 21,211)( 22,212)( 23,213)
( 24,214)( 25,215)( 26,216)( 27,217)( 28,218)( 29,219)( 30,220)( 31,221)
( 32,222)( 33,223)( 34,224)( 35,225)( 36,226)( 37,227)( 38,228)( 39,400)
( 40,401)( 41,402)( 42,403)( 43,404)( 44,405)( 45,406)( 46,407)( 47,408)
( 48,409)( 49,410)( 50,411)( 51,412)( 52,413)( 53,414)( 54,415)( 55,416)
( 56,417)( 57,418)( 58,381)( 59,382)( 60,383)( 61,384)( 62,385)( 63,386)
( 64,387)( 65,388)( 66,389)( 67,390)( 68,391)( 69,392)( 70,393)( 71,394)
( 72,395)( 73,396)( 74,397)( 75,398)( 76,399)( 77,362)( 78,363)( 79,364)
( 80,365)( 81,366)( 82,367)( 83,368)( 84,369)( 85,370)( 86,371)( 87,372)
( 88,373)( 89,374)( 90,375)( 91,376)( 92,377)( 93,378)( 94,379)( 95,380)
( 96,343)( 97,344)( 98,345)( 99,346)(100,347)(101,348)(102,349)(103,350)
(104,351)(105,352)(106,353)(107,354)(108,355)(109,356)(110,357)(111,358)
(112,359)(113,360)(114,361)(115,324)(116,325)(117,326)(118,327)(119,328)
(120,329)(121,330)(122,331)(123,332)(124,333)(125,334)(126,335)(127,336)
(128,337)(129,338)(130,339)(131,340)(132,341)(133,342)(134,305)(135,306)
(136,307)(137,308)(138,309)(139,310)(140,311)(141,312)(142,313)(143,314)
(144,315)(145,316)(146,317)(147,318)(148,319)(149,320)(150,321)(151,322)
(152,323)(153,286)(154,287)(155,288)(156,289)(157,290)(158,291)(159,292)
(160,293)(161,294)(162,295)(163,296)(164,297)(165,298)(166,299)(167,300)
(168,301)(169,302)(170,303)(171,304)(172,267)(173,268)(174,269)(175,270)
(176,271)(177,272)(178,273)(179,274)(180,275)(181,276)(182,277)(183,278)
(184,279)(185,280)(186,281)(187,282)(188,283)(189,284)(190,285)(191,248)
(192,249)(193,250)(194,251)(195,252)(196,253)(197,254)(198,255)(199,256)
(200,257)(201,258)(202,259)(203,260)(204,261)(205,262)(206,263)(207,264)
(208,265)(209,266);
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,
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