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