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Polytope of Type {8,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,102}*1632
Also Known As : {8,102|2}. if this polytope has another name.
Group : SmallGroup(1632,871)
Rank : 3
Schlafli Type : {8,102}
Number of vertices, edges, etc : 8, 408, 102
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 : {4,102}*816a
   3-fold quotients : {8,34}*544
   4-fold quotients : {2,102}*408
   6-fold quotients : {4,34}*272
   8-fold quotients : {2,51}*204
   12-fold quotients : {2,34}*136
   17-fold quotients : {8,6}*96
   24-fold quotients : {2,17}*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 := (103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)
(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)
(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)
(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)(134,185)
(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)(142,193)
(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)
(151,202)(152,203)(153,204)(205,307)(206,308)(207,309)(208,310)(209,311)
(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)(216,318)(217,319)
(218,320)(219,321)(220,322)(221,323)(222,324)(223,325)(224,326)(225,327)
(226,328)(227,329)(228,330)(229,331)(230,332)(231,333)(232,334)(233,335)
(234,336)(235,337)(236,338)(237,339)(238,340)(239,341)(240,342)(241,343)
(242,344)(243,345)(244,346)(245,347)(246,348)(247,349)(248,350)(249,351)
(250,352)(251,353)(252,354)(253,355)(254,356)(255,357)(256,358)(257,359)
(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)(264,366)(265,367)
(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)(272,374)(273,375)
(274,376)(275,377)(276,378)(277,379)(278,380)(279,381)(280,382)(281,383)
(282,384)(283,385)(284,386)(285,387)(286,388)(287,389)(288,390)(289,391)
(290,392)(291,393)(292,394)(293,395)(294,396)(295,397)(296,398)(297,399)
(298,400)(299,401)(300,402)(301,403)(302,404)(303,405)(304,406)(305,407)
(306,408);;
s1 := (  1,205)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)
(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)( 24,250)
( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)( 32,242)
( 33,241)( 34,240)( 35,222)( 36,238)( 37,237)( 38,236)( 39,235)( 40,234)
( 41,233)( 42,232)( 43,231)( 44,230)( 45,229)( 46,228)( 47,227)( 48,226)
( 49,225)( 50,224)( 51,223)( 52,256)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)
( 65,260)( 66,259)( 67,258)( 68,257)( 69,290)( 70,306)( 71,305)( 72,304)
( 73,303)( 74,302)( 75,301)( 76,300)( 77,299)( 78,298)( 79,297)( 80,296)
( 81,295)( 82,294)( 83,293)( 84,292)( 85,291)( 86,273)( 87,289)( 88,288)
( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)
( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,358)(104,374)
(105,373)(106,372)(107,371)(108,370)(109,369)(110,368)(111,367)(112,366)
(113,365)(114,364)(115,363)(116,362)(117,361)(118,360)(119,359)(120,392)
(121,408)(122,407)(123,406)(124,405)(125,404)(126,403)(127,402)(128,401)
(129,400)(130,399)(131,398)(132,397)(133,396)(134,395)(135,394)(136,393)
(137,375)(138,391)(139,390)(140,389)(141,388)(142,387)(143,386)(144,385)
(145,384)(146,383)(147,382)(148,381)(149,380)(150,379)(151,378)(152,377)
(153,376)(154,307)(155,323)(156,322)(157,321)(158,320)(159,319)(160,318)
(161,317)(162,316)(163,315)(164,314)(165,313)(166,312)(167,311)(168,310)
(169,309)(170,308)(171,341)(172,357)(173,356)(174,355)(175,354)(176,353)
(177,352)(178,351)(179,350)(180,349)(181,348)(182,347)(183,346)(184,345)
(185,344)(186,343)(187,342)(188,324)(189,340)(190,339)(191,338)(192,337)
(193,336)(194,335)(195,334)(196,333)(197,332)(198,331)(199,330)(200,329)
(201,328)(202,327)(203,326)(204,325);;
s2 := (  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)
(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)
( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52, 70)( 53, 69)( 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)
( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)
( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)
(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)
(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)(142,150)
(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)(158,185)
(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)
(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)(192,202)
(193,201)(194,200)(195,199)(196,198)(205,223)(206,222)(207,238)(208,237)
(209,236)(210,235)(211,234)(212,233)(213,232)(214,231)(215,230)(216,229)
(217,228)(218,227)(219,226)(220,225)(221,224)(239,240)(241,255)(242,254)
(243,253)(244,252)(245,251)(246,250)(247,249)(256,274)(257,273)(258,289)
(259,288)(260,287)(261,286)(262,285)(263,284)(264,283)(265,282)(266,281)
(267,280)(268,279)(269,278)(270,277)(271,276)(272,275)(290,291)(292,306)
(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)(307,325)(308,324)
(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)(341,342)
(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)(349,351)(358,376)
(359,375)(360,391)(361,390)(362,389)(363,388)(364,387)(365,386)(366,385)
(367,384)(368,383)(369,382)(370,381)(371,380)(372,379)(373,378)(374,377)
(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)(400,402);;
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, 
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*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*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(408)!(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)
(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)
(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)
(126,177)(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)
(134,185)(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)
(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)
(150,201)(151,202)(152,203)(153,204)(205,307)(206,308)(207,309)(208,310)
(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)(216,318)
(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,325)(224,326)
(225,327)(226,328)(227,329)(228,330)(229,331)(230,332)(231,333)(232,334)
(233,335)(234,336)(235,337)(236,338)(237,339)(238,340)(239,341)(240,342)
(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,349)(248,350)
(249,351)(250,352)(251,353)(252,354)(253,355)(254,356)(255,357)(256,358)
(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)(264,366)
(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)(272,374)
(273,375)(274,376)(275,377)(276,378)(277,379)(278,380)(279,381)(280,382)
(281,383)(282,384)(283,385)(284,386)(285,387)(286,388)(287,389)(288,390)
(289,391)(290,392)(291,393)(292,394)(293,395)(294,396)(295,397)(296,398)
(297,399)(298,400)(299,401)(300,402)(301,403)(302,404)(303,405)(304,406)
(305,407)(306,408);
s1 := Sym(408)!(  1,205)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)
(  8,215)(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)
( 24,250)( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)
( 32,242)( 33,241)( 34,240)( 35,222)( 36,238)( 37,237)( 38,236)( 39,235)
( 40,234)( 41,233)( 42,232)( 43,231)( 44,230)( 45,229)( 46,228)( 47,227)
( 48,226)( 49,225)( 50,224)( 51,223)( 52,256)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)
( 64,261)( 65,260)( 66,259)( 67,258)( 68,257)( 69,290)( 70,306)( 71,305)
( 72,304)( 73,303)( 74,302)( 75,301)( 76,300)( 77,299)( 78,298)( 79,297)
( 80,296)( 81,295)( 82,294)( 83,293)( 84,292)( 85,291)( 86,273)( 87,289)
( 88,288)( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)
( 96,280)( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,358)
(104,374)(105,373)(106,372)(107,371)(108,370)(109,369)(110,368)(111,367)
(112,366)(113,365)(114,364)(115,363)(116,362)(117,361)(118,360)(119,359)
(120,392)(121,408)(122,407)(123,406)(124,405)(125,404)(126,403)(127,402)
(128,401)(129,400)(130,399)(131,398)(132,397)(133,396)(134,395)(135,394)
(136,393)(137,375)(138,391)(139,390)(140,389)(141,388)(142,387)(143,386)
(144,385)(145,384)(146,383)(147,382)(148,381)(149,380)(150,379)(151,378)
(152,377)(153,376)(154,307)(155,323)(156,322)(157,321)(158,320)(159,319)
(160,318)(161,317)(162,316)(163,315)(164,314)(165,313)(166,312)(167,311)
(168,310)(169,309)(170,308)(171,341)(172,357)(173,356)(174,355)(175,354)
(176,353)(177,352)(178,351)(179,350)(180,349)(181,348)(182,347)(183,346)
(184,345)(185,344)(186,343)(187,342)(188,324)(189,340)(190,339)(191,338)
(192,337)(193,336)(194,335)(195,334)(196,333)(197,332)(198,331)(199,330)
(200,329)(201,328)(202,327)(203,326)(204,325);
s2 := Sym(408)!(  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)
(  8, 29)(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)
( 16, 21)( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)
( 42, 46)( 43, 45)( 52, 70)( 53, 69)( 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)( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)
( 92, 98)( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)
(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)
(116,125)(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)
(142,150)(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)
(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)
(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)
(192,202)(193,201)(194,200)(195,199)(196,198)(205,223)(206,222)(207,238)
(208,237)(209,236)(210,235)(211,234)(212,233)(213,232)(214,231)(215,230)
(216,229)(217,228)(218,227)(219,226)(220,225)(221,224)(239,240)(241,255)
(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(256,274)(257,273)
(258,289)(259,288)(260,287)(261,286)(262,285)(263,284)(264,283)(265,282)
(266,281)(267,280)(268,279)(269,278)(270,277)(271,276)(272,275)(290,291)
(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)(307,325)
(308,324)(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)
(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)(349,351)
(358,376)(359,375)(360,391)(361,390)(362,389)(363,388)(364,387)(365,386)
(366,385)(367,384)(368,383)(369,382)(370,381)(371,380)(372,379)(373,378)
(374,377)(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)
(400,402);
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, 
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*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*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