Polytope of Type {102,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,6}*1632
if this polytope has a name.
Group : SmallGroup(1632,1195)
Rank : 3
Schlafli Type : {102,6}
Number of vertices, edges, etc : 136, 408, 8
Order of s₀s₁s₂ : 68
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {51,6}*816
   12-fold quotients : {34,2}*136
   17-fold quotients : {6,6}*96
   24-fold quotients : {17,2}*68
   34-fold quotients : {3,6}*48, {6,3}*48
   68-fold quotients : {3,3}*24
   204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope