Polytope of Type {22,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,36}*1584
Also Known As : {22,36|2}. if this polytope has another name.
Group : SmallGroup(1584,113)
Rank : 3
Schlafli Type : {22,36}
Number of vertices, edges, etc : 22, 396, 36
Order of s0s1s2 : 396
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 : {22,18}*792
   3-fold quotients : {22,12}*528
   6-fold quotients : {22,6}*264
   9-fold quotients : {22,4}*176
   11-fold quotients : {2,36}*144
   18-fold quotients : {22,2}*88
   22-fold quotients : {2,18}*72
   33-fold quotients : {2,12}*48
   36-fold quotients : {11,2}*44
   44-fold quotients : {2,9}*36
   66-fold quotients : {2,6}*24
   99-fold quotients : {2,4}*16
   132-fold quotients : {2,3}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  4, 31)(  5, 32)(  6, 33)(  7, 28)(  8, 29)(  9, 30)( 10, 25)( 11, 26)
( 12, 27)( 13, 22)( 14, 23)( 15, 24)( 16, 19)( 17, 20)( 18, 21)( 37, 64)
( 38, 65)( 39, 66)( 40, 61)( 41, 62)( 42, 63)( 43, 58)( 44, 59)( 45, 60)
( 46, 55)( 47, 56)( 48, 57)( 49, 52)( 50, 53)( 51, 54)( 70, 97)( 71, 98)
( 72, 99)( 73, 94)( 74, 95)( 75, 96)( 76, 91)( 77, 92)( 78, 93)( 79, 88)
( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)(103,130)(104,131)(105,132)
(106,127)(107,128)(108,129)(109,124)(110,125)(111,126)(112,121)(113,122)
(114,123)(115,118)(116,119)(117,120)(136,163)(137,164)(138,165)(139,160)
(140,161)(141,162)(142,157)(143,158)(144,159)(145,154)(146,155)(147,156)
(148,151)(149,152)(150,153)(169,196)(170,197)(171,198)(172,193)(173,194)
(174,195)(175,190)(176,191)(177,192)(178,187)(179,188)(180,189)(181,184)
(182,185)(183,186)(202,229)(203,230)(204,231)(205,226)(206,227)(207,228)
(208,223)(209,224)(210,225)(211,220)(212,221)(213,222)(214,217)(215,218)
(216,219)(235,262)(236,263)(237,264)(238,259)(239,260)(240,261)(241,256)
(242,257)(243,258)(244,253)(245,254)(246,255)(247,250)(248,251)(249,252)
(268,295)(269,296)(270,297)(271,292)(272,293)(273,294)(274,289)(275,290)
(276,291)(277,286)(278,287)(279,288)(280,283)(281,284)(282,285)(301,328)
(302,329)(303,330)(304,325)(305,326)(306,327)(307,322)(308,323)(309,324)
(310,319)(311,320)(312,321)(313,316)(314,317)(315,318)(334,361)(335,362)
(336,363)(337,358)(338,359)(339,360)(340,355)(341,356)(342,357)(343,352)
(344,353)(345,354)(346,349)(347,350)(348,351)(367,394)(368,395)(369,396)
(370,391)(371,392)(372,393)(373,388)(374,389)(375,390)(376,385)(377,386)
(378,387)(379,382)(380,383)(381,384);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7, 31)(  8, 33)(  9, 32)( 10, 28)( 11, 30)
( 12, 29)( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 20, 21)
( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)( 49, 90)
( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)
( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)(100,103)(101,105)(102,104)(106,130)(107,132)(108,131)(109,127)
(110,129)(111,128)(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)
(119,120)(133,171)(134,170)(135,169)(136,168)(137,167)(138,166)(139,198)
(140,197)(141,196)(142,195)(143,194)(144,193)(145,192)(146,191)(147,190)
(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,183)(155,182)
(156,181)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)
(164,173)(165,172)(199,301)(200,303)(201,302)(202,298)(203,300)(204,299)
(205,328)(206,330)(207,329)(208,325)(209,327)(210,326)(211,322)(212,324)
(213,323)(214,319)(215,321)(216,320)(217,316)(218,318)(219,317)(220,313)
(221,315)(222,314)(223,310)(224,312)(225,311)(226,307)(227,309)(228,308)
(229,304)(230,306)(231,305)(232,369)(233,368)(234,367)(235,366)(236,365)
(237,364)(238,396)(239,395)(240,394)(241,393)(242,392)(243,391)(244,390)
(245,389)(246,388)(247,387)(248,386)(249,385)(250,384)(251,383)(252,382)
(253,381)(254,380)(255,379)(256,378)(257,377)(258,376)(259,375)(260,374)
(261,373)(262,372)(263,371)(264,370)(265,336)(266,335)(267,334)(268,333)
(269,332)(270,331)(271,363)(272,362)(273,361)(274,360)(275,359)(276,358)
(277,357)(278,356)(279,355)(280,354)(281,353)(282,352)(283,351)(284,350)
(285,349)(286,348)(287,347)(288,346)(289,345)(290,344)(291,343)(292,342)
(293,341)(294,340)(295,339)(296,338)(297,337);;
s2 := (  1,232)(  2,234)(  3,233)(  4,235)(  5,237)(  6,236)(  7,238)(  8,240)
(  9,239)( 10,241)( 11,243)( 12,242)( 13,244)( 14,246)( 15,245)( 16,247)
( 17,249)( 18,248)( 19,250)( 20,252)( 21,251)( 22,253)( 23,255)( 24,254)
( 25,256)( 26,258)( 27,257)( 28,259)( 29,261)( 30,260)( 31,262)( 32,264)
( 33,263)( 34,199)( 35,201)( 36,200)( 37,202)( 38,204)( 39,203)( 40,205)
( 41,207)( 42,206)( 43,208)( 44,210)( 45,209)( 46,211)( 47,213)( 48,212)
( 49,214)( 50,216)( 51,215)( 52,217)( 53,219)( 54,218)( 55,220)( 56,222)
( 57,221)( 58,223)( 59,225)( 60,224)( 61,226)( 62,228)( 63,227)( 64,229)
( 65,231)( 66,230)( 67,267)( 68,266)( 69,265)( 70,270)( 71,269)( 72,268)
( 73,273)( 74,272)( 75,271)( 76,276)( 77,275)( 78,274)( 79,279)( 80,278)
( 81,277)( 82,282)( 83,281)( 84,280)( 85,285)( 86,284)( 87,283)( 88,288)
( 89,287)( 90,286)( 91,291)( 92,290)( 93,289)( 94,294)( 95,293)( 96,292)
( 97,297)( 98,296)( 99,295)(100,331)(101,333)(102,332)(103,334)(104,336)
(105,335)(106,337)(107,339)(108,338)(109,340)(110,342)(111,341)(112,343)
(113,345)(114,344)(115,346)(116,348)(117,347)(118,349)(119,351)(120,350)
(121,352)(122,354)(123,353)(124,355)(125,357)(126,356)(127,358)(128,360)
(129,359)(130,361)(131,363)(132,362)(133,298)(134,300)(135,299)(136,301)
(137,303)(138,302)(139,304)(140,306)(141,305)(142,307)(143,309)(144,308)
(145,310)(146,312)(147,311)(148,313)(149,315)(150,314)(151,316)(152,318)
(153,317)(154,319)(155,321)(156,320)(157,322)(158,324)(159,323)(160,325)
(161,327)(162,326)(163,328)(164,330)(165,329)(166,366)(167,365)(168,364)
(169,369)(170,368)(171,367)(172,372)(173,371)(174,370)(175,375)(176,374)
(177,373)(178,378)(179,377)(180,376)(181,381)(182,380)(183,379)(184,384)
(185,383)(186,382)(187,387)(188,386)(189,385)(190,390)(191,389)(192,388)
(193,393)(194,392)(195,391)(196,396)(197,395)(198,394);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(396)!(  4, 31)(  5, 32)(  6, 33)(  7, 28)(  8, 29)(  9, 30)( 10, 25)
( 11, 26)( 12, 27)( 13, 22)( 14, 23)( 15, 24)( 16, 19)( 17, 20)( 18, 21)
( 37, 64)( 38, 65)( 39, 66)( 40, 61)( 41, 62)( 42, 63)( 43, 58)( 44, 59)
( 45, 60)( 46, 55)( 47, 56)( 48, 57)( 49, 52)( 50, 53)( 51, 54)( 70, 97)
( 71, 98)( 72, 99)( 73, 94)( 74, 95)( 75, 96)( 76, 91)( 77, 92)( 78, 93)
( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)(103,130)(104,131)
(105,132)(106,127)(107,128)(108,129)(109,124)(110,125)(111,126)(112,121)
(113,122)(114,123)(115,118)(116,119)(117,120)(136,163)(137,164)(138,165)
(139,160)(140,161)(141,162)(142,157)(143,158)(144,159)(145,154)(146,155)
(147,156)(148,151)(149,152)(150,153)(169,196)(170,197)(171,198)(172,193)
(173,194)(174,195)(175,190)(176,191)(177,192)(178,187)(179,188)(180,189)
(181,184)(182,185)(183,186)(202,229)(203,230)(204,231)(205,226)(206,227)
(207,228)(208,223)(209,224)(210,225)(211,220)(212,221)(213,222)(214,217)
(215,218)(216,219)(235,262)(236,263)(237,264)(238,259)(239,260)(240,261)
(241,256)(242,257)(243,258)(244,253)(245,254)(246,255)(247,250)(248,251)
(249,252)(268,295)(269,296)(270,297)(271,292)(272,293)(273,294)(274,289)
(275,290)(276,291)(277,286)(278,287)(279,288)(280,283)(281,284)(282,285)
(301,328)(302,329)(303,330)(304,325)(305,326)(306,327)(307,322)(308,323)
(309,324)(310,319)(311,320)(312,321)(313,316)(314,317)(315,318)(334,361)
(335,362)(336,363)(337,358)(338,359)(339,360)(340,355)(341,356)(342,357)
(343,352)(344,353)(345,354)(346,349)(347,350)(348,351)(367,394)(368,395)
(369,396)(370,391)(371,392)(372,393)(373,388)(374,389)(375,390)(376,385)
(377,386)(378,387)(379,382)(380,383)(381,384);
s1 := Sym(396)!(  1,  4)(  2,  6)(  3,  5)(  7, 31)(  8, 33)(  9, 32)( 10, 28)
( 11, 30)( 12, 29)( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)
( 20, 21)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)( 40, 99)
( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)
( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)
( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)(100,103)(101,105)(102,104)(106,130)(107,132)(108,131)
(109,127)(110,129)(111,128)(112,124)(113,126)(114,125)(115,121)(116,123)
(117,122)(119,120)(133,171)(134,170)(135,169)(136,168)(137,167)(138,166)
(139,198)(140,197)(141,196)(142,195)(143,194)(144,193)(145,192)(146,191)
(147,190)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,183)
(155,182)(156,181)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)
(163,174)(164,173)(165,172)(199,301)(200,303)(201,302)(202,298)(203,300)
(204,299)(205,328)(206,330)(207,329)(208,325)(209,327)(210,326)(211,322)
(212,324)(213,323)(214,319)(215,321)(216,320)(217,316)(218,318)(219,317)
(220,313)(221,315)(222,314)(223,310)(224,312)(225,311)(226,307)(227,309)
(228,308)(229,304)(230,306)(231,305)(232,369)(233,368)(234,367)(235,366)
(236,365)(237,364)(238,396)(239,395)(240,394)(241,393)(242,392)(243,391)
(244,390)(245,389)(246,388)(247,387)(248,386)(249,385)(250,384)(251,383)
(252,382)(253,381)(254,380)(255,379)(256,378)(257,377)(258,376)(259,375)
(260,374)(261,373)(262,372)(263,371)(264,370)(265,336)(266,335)(267,334)
(268,333)(269,332)(270,331)(271,363)(272,362)(273,361)(274,360)(275,359)
(276,358)(277,357)(278,356)(279,355)(280,354)(281,353)(282,352)(283,351)
(284,350)(285,349)(286,348)(287,347)(288,346)(289,345)(290,344)(291,343)
(292,342)(293,341)(294,340)(295,339)(296,338)(297,337);
s2 := Sym(396)!(  1,232)(  2,234)(  3,233)(  4,235)(  5,237)(  6,236)(  7,238)
(  8,240)(  9,239)( 10,241)( 11,243)( 12,242)( 13,244)( 14,246)( 15,245)
( 16,247)( 17,249)( 18,248)( 19,250)( 20,252)( 21,251)( 22,253)( 23,255)
( 24,254)( 25,256)( 26,258)( 27,257)( 28,259)( 29,261)( 30,260)( 31,262)
( 32,264)( 33,263)( 34,199)( 35,201)( 36,200)( 37,202)( 38,204)( 39,203)
( 40,205)( 41,207)( 42,206)( 43,208)( 44,210)( 45,209)( 46,211)( 47,213)
( 48,212)( 49,214)( 50,216)( 51,215)( 52,217)( 53,219)( 54,218)( 55,220)
( 56,222)( 57,221)( 58,223)( 59,225)( 60,224)( 61,226)( 62,228)( 63,227)
( 64,229)( 65,231)( 66,230)( 67,267)( 68,266)( 69,265)( 70,270)( 71,269)
( 72,268)( 73,273)( 74,272)( 75,271)( 76,276)( 77,275)( 78,274)( 79,279)
( 80,278)( 81,277)( 82,282)( 83,281)( 84,280)( 85,285)( 86,284)( 87,283)
( 88,288)( 89,287)( 90,286)( 91,291)( 92,290)( 93,289)( 94,294)( 95,293)
( 96,292)( 97,297)( 98,296)( 99,295)(100,331)(101,333)(102,332)(103,334)
(104,336)(105,335)(106,337)(107,339)(108,338)(109,340)(110,342)(111,341)
(112,343)(113,345)(114,344)(115,346)(116,348)(117,347)(118,349)(119,351)
(120,350)(121,352)(122,354)(123,353)(124,355)(125,357)(126,356)(127,358)
(128,360)(129,359)(130,361)(131,363)(132,362)(133,298)(134,300)(135,299)
(136,301)(137,303)(138,302)(139,304)(140,306)(141,305)(142,307)(143,309)
(144,308)(145,310)(146,312)(147,311)(148,313)(149,315)(150,314)(151,316)
(152,318)(153,317)(154,319)(155,321)(156,320)(157,322)(158,324)(159,323)
(160,325)(161,327)(162,326)(163,328)(164,330)(165,329)(166,366)(167,365)
(168,364)(169,369)(170,368)(171,367)(172,372)(173,371)(174,370)(175,375)
(176,374)(177,373)(178,378)(179,377)(180,376)(181,381)(182,380)(183,379)
(184,384)(185,383)(186,382)(187,387)(188,386)(189,385)(190,390)(191,389)
(192,388)(193,393)(194,392)(195,391)(196,396)(197,395)(198,394);
poly := sub<Sym(396)|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 >;
References : None.
to this polytope