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Polytope of Type {6,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,102}*1632
if this polytope has a name.
Group : SmallGroup(1632,1195)
Rank : 3
Schlafli Type : {6,102}
Number of vertices, edges, etc : 8, 408, 136
Order of s0s1s2 : 68
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,51}*816
   12-fold quotients : {2,34}*136
   17-fold quotients : {6,6}*96
   24-fold quotients : {2,17}*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)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 63, 64)
( 67, 68)( 69,137)( 70,138)( 71,140)( 72,139)( 73,141)( 74,142)( 75,144)
( 76,143)( 77,145)( 78,146)( 79,148)( 80,147)( 81,149)( 82,150)( 83,152)
( 84,151)( 85,153)( 86,154)( 87,156)( 88,155)( 89,157)( 90,158)( 91,160)
( 92,159)( 93,161)( 94,162)( 95,164)( 96,163)( 97,165)( 98,166)( 99,168)
(100,167)(101,169)(102,170)(103,172)(104,171)(105,173)(106,174)(107,176)
(108,175)(109,177)(110,178)(111,180)(112,179)(113,181)(114,182)(115,184)
(116,183)(117,185)(118,186)(119,188)(120,187)(121,189)(122,190)(123,192)
(124,191)(125,193)(126,194)(127,196)(128,195)(129,197)(130,198)(131,200)
(132,199)(133,201)(134,202)(135,204)(136,203)(207,208)(211,212)(215,216)
(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(243,244)(247,248)
(251,252)(255,256)(259,260)(263,264)(267,268)(271,272)(273,341)(274,342)
(275,344)(276,343)(277,345)(278,346)(279,348)(280,347)(281,349)(282,350)
(283,352)(284,351)(285,353)(286,354)(287,356)(288,355)(289,357)(290,358)
(291,360)(292,359)(293,361)(294,362)(295,364)(296,363)(297,365)(298,366)
(299,368)(300,367)(301,369)(302,370)(303,372)(304,371)(305,373)(306,374)
(307,376)(308,375)(309,377)(310,378)(311,380)(312,379)(313,381)(314,382)
(315,384)(316,383)(317,385)(318,386)(319,388)(320,387)(321,389)(322,390)
(323,392)(324,391)(325,393)(326,394)(327,396)(328,395)(329,397)(330,398)
(331,400)(332,399)(333,401)(334,402)(335,404)(336,403)(337,405)(338,406)
(339,408)(340,407);;
s1 := (  1, 69)(  2, 72)(  3, 71)(  4, 70)(  5,133)(  6,136)(  7,135)(  8,134)
(  9,129)( 10,132)( 11,131)( 12,130)( 13,125)( 14,128)( 15,127)( 16,126)
( 17,121)( 18,124)( 19,123)( 20,122)( 21,117)( 22,120)( 23,119)( 24,118)
( 25,113)( 26,116)( 27,115)( 28,114)( 29,109)( 30,112)( 31,111)( 32,110)
( 33,105)( 34,108)( 35,107)( 36,106)( 37,101)( 38,104)( 39,103)( 40,102)
( 41, 97)( 42,100)( 43, 99)( 44, 98)( 45, 93)( 46, 96)( 47, 95)( 48, 94)
( 49, 89)( 50, 92)( 51, 91)( 52, 90)( 53, 85)( 54, 88)( 55, 87)( 56, 86)
( 57, 81)( 58, 84)( 59, 83)( 60, 82)( 61, 77)( 62, 80)( 63, 79)( 64, 78)
( 65, 73)( 66, 76)( 67, 75)( 68, 74)(138,140)(141,201)(142,204)(143,203)
(144,202)(145,197)(146,200)(147,199)(148,198)(149,193)(150,196)(151,195)
(152,194)(153,189)(154,192)(155,191)(156,190)(157,185)(158,188)(159,187)
(160,186)(161,181)(162,184)(163,183)(164,182)(165,177)(166,180)(167,179)
(168,178)(169,173)(170,176)(171,175)(172,174)(205,273)(206,276)(207,275)
(208,274)(209,337)(210,340)(211,339)(212,338)(213,333)(214,336)(215,335)
(216,334)(217,329)(218,332)(219,331)(220,330)(221,325)(222,328)(223,327)
(224,326)(225,321)(226,324)(227,323)(228,322)(229,317)(230,320)(231,319)
(232,318)(233,313)(234,316)(235,315)(236,314)(237,309)(238,312)(239,311)
(240,310)(241,305)(242,308)(243,307)(244,306)(245,301)(246,304)(247,303)
(248,302)(249,297)(250,300)(251,299)(252,298)(253,293)(254,296)(255,295)
(256,294)(257,289)(258,292)(259,291)(260,290)(261,285)(262,288)(263,287)
(264,286)(265,281)(266,284)(267,283)(268,282)(269,277)(270,280)(271,279)
(272,278)(342,344)(345,405)(346,408)(347,407)(348,406)(349,401)(350,404)
(351,403)(352,402)(353,397)(354,400)(355,399)(356,398)(357,393)(358,396)
(359,395)(360,394)(361,389)(362,392)(363,391)(364,390)(365,385)(366,388)
(367,387)(368,386)(369,381)(370,384)(371,383)(372,382)(373,377)(374,380)
(375,379)(376,378);;
s2 := (  1,210)(  2,209)(  3,211)(  4,212)(  5,206)(  6,205)(  7,207)(  8,208)
(  9,270)( 10,269)( 11,271)( 12,272)( 13,266)( 14,265)( 15,267)( 16,268)
( 17,262)( 18,261)( 19,263)( 20,264)( 21,258)( 22,257)( 23,259)( 24,260)
( 25,254)( 26,253)( 27,255)( 28,256)( 29,250)( 30,249)( 31,251)( 32,252)
( 33,246)( 34,245)( 35,247)( 36,248)( 37,242)( 38,241)( 39,243)( 40,244)
( 41,238)( 42,237)( 43,239)( 44,240)( 45,234)( 46,233)( 47,235)( 48,236)
( 49,230)( 50,229)( 51,231)( 52,232)( 53,226)( 54,225)( 55,227)( 56,228)
( 57,222)( 58,221)( 59,223)( 60,224)( 61,218)( 62,217)( 63,219)( 64,220)
( 65,214)( 66,213)( 67,215)( 68,216)( 69,346)( 70,345)( 71,347)( 72,348)
( 73,342)( 74,341)( 75,343)( 76,344)( 77,406)( 78,405)( 79,407)( 80,408)
( 81,402)( 82,401)( 83,403)( 84,404)( 85,398)( 86,397)( 87,399)( 88,400)
( 89,394)( 90,393)( 91,395)( 92,396)( 93,390)( 94,389)( 95,391)( 96,392)
( 97,386)( 98,385)( 99,387)(100,388)(101,382)(102,381)(103,383)(104,384)
(105,378)(106,377)(107,379)(108,380)(109,374)(110,373)(111,375)(112,376)
(113,370)(114,369)(115,371)(116,372)(117,366)(118,365)(119,367)(120,368)
(121,362)(122,361)(123,363)(124,364)(125,358)(126,357)(127,359)(128,360)
(129,354)(130,353)(131,355)(132,356)(133,350)(134,349)(135,351)(136,352)
(137,278)(138,277)(139,279)(140,280)(141,274)(142,273)(143,275)(144,276)
(145,338)(146,337)(147,339)(148,340)(149,334)(150,333)(151,335)(152,336)
(153,330)(154,329)(155,331)(156,332)(157,326)(158,325)(159,327)(160,328)
(161,322)(162,321)(163,323)(164,324)(165,318)(166,317)(167,319)(168,320)
(169,314)(170,313)(171,315)(172,316)(173,310)(174,309)(175,311)(176,312)
(177,306)(178,305)(179,307)(180,308)(181,302)(182,301)(183,303)(184,304)
(185,298)(186,297)(187,299)(188,300)(189,294)(190,293)(191,295)(192,296)
(193,290)(194,289)(195,291)(196,292)(197,286)(198,285)(199,287)(200,288)
(201,282)(202,281)(203,283)(204,284);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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*s0*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*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(408)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)
( 63, 64)( 67, 68)( 69,137)( 70,138)( 71,140)( 72,139)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,145)( 78,146)( 79,148)( 80,147)( 81,149)( 82,150)
( 83,152)( 84,151)( 85,153)( 86,154)( 87,156)( 88,155)( 89,157)( 90,158)
( 91,160)( 92,159)( 93,161)( 94,162)( 95,164)( 96,163)( 97,165)( 98,166)
( 99,168)(100,167)(101,169)(102,170)(103,172)(104,171)(105,173)(106,174)
(107,176)(108,175)(109,177)(110,178)(111,180)(112,179)(113,181)(114,182)
(115,184)(116,183)(117,185)(118,186)(119,188)(120,187)(121,189)(122,190)
(123,192)(124,191)(125,193)(126,194)(127,196)(128,195)(129,197)(130,198)
(131,200)(132,199)(133,201)(134,202)(135,204)(136,203)(207,208)(211,212)
(215,216)(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)(243,244)
(247,248)(251,252)(255,256)(259,260)(263,264)(267,268)(271,272)(273,341)
(274,342)(275,344)(276,343)(277,345)(278,346)(279,348)(280,347)(281,349)
(282,350)(283,352)(284,351)(285,353)(286,354)(287,356)(288,355)(289,357)
(290,358)(291,360)(292,359)(293,361)(294,362)(295,364)(296,363)(297,365)
(298,366)(299,368)(300,367)(301,369)(302,370)(303,372)(304,371)(305,373)
(306,374)(307,376)(308,375)(309,377)(310,378)(311,380)(312,379)(313,381)
(314,382)(315,384)(316,383)(317,385)(318,386)(319,388)(320,387)(321,389)
(322,390)(323,392)(324,391)(325,393)(326,394)(327,396)(328,395)(329,397)
(330,398)(331,400)(332,399)(333,401)(334,402)(335,404)(336,403)(337,405)
(338,406)(339,408)(340,407);
s1 := Sym(408)!(  1, 69)(  2, 72)(  3, 71)(  4, 70)(  5,133)(  6,136)(  7,135)
(  8,134)(  9,129)( 10,132)( 11,131)( 12,130)( 13,125)( 14,128)( 15,127)
( 16,126)( 17,121)( 18,124)( 19,123)( 20,122)( 21,117)( 22,120)( 23,119)
( 24,118)( 25,113)( 26,116)( 27,115)( 28,114)( 29,109)( 30,112)( 31,111)
( 32,110)( 33,105)( 34,108)( 35,107)( 36,106)( 37,101)( 38,104)( 39,103)
( 40,102)( 41, 97)( 42,100)( 43, 99)( 44, 98)( 45, 93)( 46, 96)( 47, 95)
( 48, 94)( 49, 89)( 50, 92)( 51, 91)( 52, 90)( 53, 85)( 54, 88)( 55, 87)
( 56, 86)( 57, 81)( 58, 84)( 59, 83)( 60, 82)( 61, 77)( 62, 80)( 63, 79)
( 64, 78)( 65, 73)( 66, 76)( 67, 75)( 68, 74)(138,140)(141,201)(142,204)
(143,203)(144,202)(145,197)(146,200)(147,199)(148,198)(149,193)(150,196)
(151,195)(152,194)(153,189)(154,192)(155,191)(156,190)(157,185)(158,188)
(159,187)(160,186)(161,181)(162,184)(163,183)(164,182)(165,177)(166,180)
(167,179)(168,178)(169,173)(170,176)(171,175)(172,174)(205,273)(206,276)
(207,275)(208,274)(209,337)(210,340)(211,339)(212,338)(213,333)(214,336)
(215,335)(216,334)(217,329)(218,332)(219,331)(220,330)(221,325)(222,328)
(223,327)(224,326)(225,321)(226,324)(227,323)(228,322)(229,317)(230,320)
(231,319)(232,318)(233,313)(234,316)(235,315)(236,314)(237,309)(238,312)
(239,311)(240,310)(241,305)(242,308)(243,307)(244,306)(245,301)(246,304)
(247,303)(248,302)(249,297)(250,300)(251,299)(252,298)(253,293)(254,296)
(255,295)(256,294)(257,289)(258,292)(259,291)(260,290)(261,285)(262,288)
(263,287)(264,286)(265,281)(266,284)(267,283)(268,282)(269,277)(270,280)
(271,279)(272,278)(342,344)(345,405)(346,408)(347,407)(348,406)(349,401)
(350,404)(351,403)(352,402)(353,397)(354,400)(355,399)(356,398)(357,393)
(358,396)(359,395)(360,394)(361,389)(362,392)(363,391)(364,390)(365,385)
(366,388)(367,387)(368,386)(369,381)(370,384)(371,383)(372,382)(373,377)
(374,380)(375,379)(376,378);
s2 := Sym(408)!(  1,210)(  2,209)(  3,211)(  4,212)(  5,206)(  6,205)(  7,207)
(  8,208)(  9,270)( 10,269)( 11,271)( 12,272)( 13,266)( 14,265)( 15,267)
( 16,268)( 17,262)( 18,261)( 19,263)( 20,264)( 21,258)( 22,257)( 23,259)
( 24,260)( 25,254)( 26,253)( 27,255)( 28,256)( 29,250)( 30,249)( 31,251)
( 32,252)( 33,246)( 34,245)( 35,247)( 36,248)( 37,242)( 38,241)( 39,243)
( 40,244)( 41,238)( 42,237)( 43,239)( 44,240)( 45,234)( 46,233)( 47,235)
( 48,236)( 49,230)( 50,229)( 51,231)( 52,232)( 53,226)( 54,225)( 55,227)
( 56,228)( 57,222)( 58,221)( 59,223)( 60,224)( 61,218)( 62,217)( 63,219)
( 64,220)( 65,214)( 66,213)( 67,215)( 68,216)( 69,346)( 70,345)( 71,347)
( 72,348)( 73,342)( 74,341)( 75,343)( 76,344)( 77,406)( 78,405)( 79,407)
( 80,408)( 81,402)( 82,401)( 83,403)( 84,404)( 85,398)( 86,397)( 87,399)
( 88,400)( 89,394)( 90,393)( 91,395)( 92,396)( 93,390)( 94,389)( 95,391)
( 96,392)( 97,386)( 98,385)( 99,387)(100,388)(101,382)(102,381)(103,383)
(104,384)(105,378)(106,377)(107,379)(108,380)(109,374)(110,373)(111,375)
(112,376)(113,370)(114,369)(115,371)(116,372)(117,366)(118,365)(119,367)
(120,368)(121,362)(122,361)(123,363)(124,364)(125,358)(126,357)(127,359)
(128,360)(129,354)(130,353)(131,355)(132,356)(133,350)(134,349)(135,351)
(136,352)(137,278)(138,277)(139,279)(140,280)(141,274)(142,273)(143,275)
(144,276)(145,338)(146,337)(147,339)(148,340)(149,334)(150,333)(151,335)
(152,336)(153,330)(154,329)(155,331)(156,332)(157,326)(158,325)(159,327)
(160,328)(161,322)(162,321)(163,323)(164,324)(165,318)(166,317)(167,319)
(168,320)(169,314)(170,313)(171,315)(172,316)(173,310)(174,309)(175,311)
(176,312)(177,306)(178,305)(179,307)(180,308)(181,302)(182,301)(183,303)
(184,304)(185,298)(186,297)(187,299)(188,300)(189,294)(190,293)(191,295)
(192,296)(193,290)(194,289)(195,291)(196,292)(197,286)(198,285)(199,287)
(200,288)(201,282)(202,281)(203,283)(204,284);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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*s0*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*s2*s0*s1*s2*s0*s1 >; 
 
References : None.
to this polytope