Polytope of Type {136,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {136,6}*1632
Also Known As : {136,6|2}. if this polytope has another name.
Group : SmallGroup(1632,325)
Rank : 3
Schlafli Type : {136,6}
Number of vertices, edges, etc : 136, 408, 6
Order of s₀s₁s₂ : 408
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 : {68,6}*816a
   3-fold quotients : {136,2}*544
   4-fold quotients : {34,6}*408
   6-fold quotients : {68,2}*272
   12-fold quotients : {34,2}*136
   17-fold quotients : {8,6}*96
   24-fold quotients : {17,2}*68
   34-fold quotients : {4,6}*48a
   51-fold quotients : {8,2}*32
   68-fold quotients : {2,6}*24
   102-fold quotients : {4,2}*16
   136-fold quotients : {2,3}*12
   204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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