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Polytope of Type {98,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {98,8}*1568
Also Known As : {98,8|2}. if this polytope has another name.
Group : SmallGroup(1568,105)
Rank : 3
Schlafli Type : {98,8}
Number of vertices, edges, etc : 98, 392, 8
Order of s0s1s2 : 392
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 : {98,4}*784
   4-fold quotients : {98,2}*392
   7-fold quotients : {14,8}*224
   8-fold quotients : {49,2}*196
   14-fold quotients : {14,4}*112
   28-fold quotients : {14,2}*56
   49-fold quotients : {2,8}*32
   56-fold quotients : {7,2}*28
   98-fold quotients : {2,4}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  7)(  3,  6)(  4,  5)(  8, 49)(  9, 48)( 10, 47)( 11, 46)( 12, 45)
( 13, 44)( 14, 43)( 15, 42)( 16, 41)( 17, 40)( 18, 39)( 19, 38)( 20, 37)
( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 51, 56)( 52, 55)( 53, 54)( 57, 98)( 58, 97)( 59, 96)( 60, 95)( 61, 94)
( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 69, 86)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
(100,105)(101,104)(102,103)(106,147)(107,146)(108,145)(109,144)(110,143)
(111,142)(112,141)(113,140)(114,139)(115,138)(116,137)(117,136)(118,135)
(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)
(149,154)(150,153)(151,152)(155,196)(156,195)(157,194)(158,193)(159,192)
(160,191)(161,190)(162,189)(163,188)(164,187)(165,186)(166,185)(167,184)
(168,183)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176)
(198,203)(199,202)(200,201)(204,245)(205,244)(206,243)(207,242)(208,241)
(209,240)(210,239)(211,238)(212,237)(213,236)(214,235)(215,234)(216,233)
(217,232)(218,231)(219,230)(220,229)(221,228)(222,227)(223,226)(224,225)
(247,252)(248,251)(249,250)(253,294)(254,293)(255,292)(256,291)(257,290)
(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)(273,274)
(296,301)(297,300)(298,299)(302,343)(303,342)(304,341)(305,340)(306,339)
(307,338)(308,337)(309,336)(310,335)(311,334)(312,333)(313,332)(314,331)
(315,330)(316,329)(317,328)(318,327)(319,326)(320,325)(321,324)(322,323)
(345,350)(346,349)(347,348)(351,392)(352,391)(353,390)(354,389)(355,388)
(356,387)(357,386)(358,385)(359,384)(360,383)(361,382)(362,381)(363,380)
(364,379)(365,378)(366,377)(367,376)(368,375)(369,374)(370,373)(371,372);;
s1 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 49)
( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)
( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 98)
( 65, 97)( 66, 96)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 91)( 72, 90)
( 73, 89)( 74, 88)( 75, 87)( 76, 86)( 77, 85)( 78, 84)( 79, 83)( 80, 82)
( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)(106,148)
(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,196)(114,195)
(115,194)(116,193)(117,192)(118,191)(119,190)(120,189)(121,188)(122,187)
(123,186)(124,185)(125,184)(126,183)(127,182)(128,181)(129,180)(130,179)
(131,178)(132,177)(133,176)(134,175)(135,174)(136,173)(137,172)(138,171)
(139,170)(140,169)(141,168)(142,167)(143,166)(144,165)(145,164)(146,163)
(147,162)(197,302)(198,308)(199,307)(200,306)(201,305)(202,304)(203,303)
(204,295)(205,301)(206,300)(207,299)(208,298)(209,297)(210,296)(211,343)
(212,342)(213,341)(214,340)(215,339)(216,338)(217,337)(218,336)(219,335)
(220,334)(221,333)(222,332)(223,331)(224,330)(225,329)(226,328)(227,327)
(228,326)(229,325)(230,324)(231,323)(232,322)(233,321)(234,320)(235,319)
(236,318)(237,317)(238,316)(239,315)(240,314)(241,313)(242,312)(243,311)
(244,310)(245,309)(246,351)(247,357)(248,356)(249,355)(250,354)(251,353)
(252,352)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)(259,345)
(260,392)(261,391)(262,390)(263,389)(264,388)(265,387)(266,386)(267,385)
(268,384)(269,383)(270,382)(271,381)(272,380)(273,379)(274,378)(275,377)
(276,376)(277,375)(278,374)(279,373)(280,372)(281,371)(282,370)(283,369)
(284,368)(285,367)(286,366)(287,365)(288,364)(289,363)(290,362)(291,361)
(292,360)(293,359)(294,358);;
s2 := (  1,197)(  2,198)(  3,199)(  4,200)(  5,201)(  6,202)(  7,203)(  8,204)
(  9,205)( 10,206)( 11,207)( 12,208)( 13,209)( 14,210)( 15,211)( 16,212)
( 17,213)( 18,214)( 19,215)( 20,216)( 21,217)( 22,218)( 23,219)( 24,220)
( 25,221)( 26,222)( 27,223)( 28,224)( 29,225)( 30,226)( 31,227)( 32,228)
( 33,229)( 34,230)( 35,231)( 36,232)( 37,233)( 38,234)( 39,235)( 40,236)
( 41,237)( 42,238)( 43,239)( 44,240)( 45,241)( 46,242)( 47,243)( 48,244)
( 49,245)( 50,246)( 51,247)( 52,248)( 53,249)( 54,250)( 55,251)( 56,252)
( 57,253)( 58,254)( 59,255)( 60,256)( 61,257)( 62,258)( 63,259)( 64,260)
( 65,261)( 66,262)( 67,263)( 68,264)( 69,265)( 70,266)( 71,267)( 72,268)
( 73,269)( 74,270)( 75,271)( 76,272)( 77,273)( 78,274)( 79,275)( 80,276)
( 81,277)( 82,278)( 83,279)( 84,280)( 85,281)( 86,282)( 87,283)( 88,284)
( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)( 96,292)
( 97,293)( 98,294)( 99,344)(100,345)(101,346)(102,347)(103,348)(104,349)
(105,350)(106,351)(107,352)(108,353)(109,354)(110,355)(111,356)(112,357)
(113,358)(114,359)(115,360)(116,361)(117,362)(118,363)(119,364)(120,365)
(121,366)(122,367)(123,368)(124,369)(125,370)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,376)(132,377)(133,378)(134,379)(135,380)(136,381)
(137,382)(138,383)(139,384)(140,385)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,391)(147,392)(148,295)(149,296)(150,297)(151,298)(152,299)
(153,300)(154,301)(155,302)(156,303)(157,304)(158,305)(159,306)(160,307)
(161,308)(162,309)(163,310)(164,311)(165,312)(166,313)(167,314)(168,315)
(169,316)(170,317)(171,318)(172,319)(173,320)(174,321)(175,322)(176,323)
(177,324)(178,325)(179,326)(180,327)(181,328)(182,329)(183,330)(184,331)
(185,332)(186,333)(187,334)(188,335)(189,336)(190,337)(191,338)(192,339)
(193,340)(194,341)(195,342)(196,343);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(392)!(  2,  7)(  3,  6)(  4,  5)(  8, 49)(  9, 48)( 10, 47)( 11, 46)
( 12, 45)( 13, 44)( 14, 43)( 15, 42)( 16, 41)( 17, 40)( 18, 39)( 19, 38)
( 20, 37)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)
( 28, 29)( 51, 56)( 52, 55)( 53, 54)( 57, 98)( 58, 97)( 59, 96)( 60, 95)
( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)
( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)(100,105)(101,104)(102,103)(106,147)(107,146)(108,145)(109,144)
(110,143)(111,142)(112,141)(113,140)(114,139)(115,138)(116,137)(117,136)
(118,135)(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)
(126,127)(149,154)(150,153)(151,152)(155,196)(156,195)(157,194)(158,193)
(159,192)(160,191)(161,190)(162,189)(163,188)(164,187)(165,186)(166,185)
(167,184)(168,183)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)
(175,176)(198,203)(199,202)(200,201)(204,245)(205,244)(206,243)(207,242)
(208,241)(209,240)(210,239)(211,238)(212,237)(213,236)(214,235)(215,234)
(216,233)(217,232)(218,231)(219,230)(220,229)(221,228)(222,227)(223,226)
(224,225)(247,252)(248,251)(249,250)(253,294)(254,293)(255,292)(256,291)
(257,290)(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)
(273,274)(296,301)(297,300)(298,299)(302,343)(303,342)(304,341)(305,340)
(306,339)(307,338)(308,337)(309,336)(310,335)(311,334)(312,333)(313,332)
(314,331)(315,330)(316,329)(317,328)(318,327)(319,326)(320,325)(321,324)
(322,323)(345,350)(346,349)(347,348)(351,392)(352,391)(353,390)(354,389)
(355,388)(356,387)(357,386)(358,385)(359,384)(360,383)(361,382)(362,381)
(363,380)(364,379)(365,378)(366,377)(367,376)(368,375)(369,374)(370,373)
(371,372);
s1 := Sym(392)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 49)( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)
( 23, 41)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)
( 31, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 98)( 65, 97)( 66, 96)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 91)
( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 76, 86)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)
(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,196)
(114,195)(115,194)(116,193)(117,192)(118,191)(119,190)(120,189)(121,188)
(122,187)(123,186)(124,185)(125,184)(126,183)(127,182)(128,181)(129,180)
(130,179)(131,178)(132,177)(133,176)(134,175)(135,174)(136,173)(137,172)
(138,171)(139,170)(140,169)(141,168)(142,167)(143,166)(144,165)(145,164)
(146,163)(147,162)(197,302)(198,308)(199,307)(200,306)(201,305)(202,304)
(203,303)(204,295)(205,301)(206,300)(207,299)(208,298)(209,297)(210,296)
(211,343)(212,342)(213,341)(214,340)(215,339)(216,338)(217,337)(218,336)
(219,335)(220,334)(221,333)(222,332)(223,331)(224,330)(225,329)(226,328)
(227,327)(228,326)(229,325)(230,324)(231,323)(232,322)(233,321)(234,320)
(235,319)(236,318)(237,317)(238,316)(239,315)(240,314)(241,313)(242,312)
(243,311)(244,310)(245,309)(246,351)(247,357)(248,356)(249,355)(250,354)
(251,353)(252,352)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)
(259,345)(260,392)(261,391)(262,390)(263,389)(264,388)(265,387)(266,386)
(267,385)(268,384)(269,383)(270,382)(271,381)(272,380)(273,379)(274,378)
(275,377)(276,376)(277,375)(278,374)(279,373)(280,372)(281,371)(282,370)
(283,369)(284,368)(285,367)(286,366)(287,365)(288,364)(289,363)(290,362)
(291,361)(292,360)(293,359)(294,358);
s2 := Sym(392)!(  1,197)(  2,198)(  3,199)(  4,200)(  5,201)(  6,202)(  7,203)
(  8,204)(  9,205)( 10,206)( 11,207)( 12,208)( 13,209)( 14,210)( 15,211)
( 16,212)( 17,213)( 18,214)( 19,215)( 20,216)( 21,217)( 22,218)( 23,219)
( 24,220)( 25,221)( 26,222)( 27,223)( 28,224)( 29,225)( 30,226)( 31,227)
( 32,228)( 33,229)( 34,230)( 35,231)( 36,232)( 37,233)( 38,234)( 39,235)
( 40,236)( 41,237)( 42,238)( 43,239)( 44,240)( 45,241)( 46,242)( 47,243)
( 48,244)( 49,245)( 50,246)( 51,247)( 52,248)( 53,249)( 54,250)( 55,251)
( 56,252)( 57,253)( 58,254)( 59,255)( 60,256)( 61,257)( 62,258)( 63,259)
( 64,260)( 65,261)( 66,262)( 67,263)( 68,264)( 69,265)( 70,266)( 71,267)
( 72,268)( 73,269)( 74,270)( 75,271)( 76,272)( 77,273)( 78,274)( 79,275)
( 80,276)( 81,277)( 82,278)( 83,279)( 84,280)( 85,281)( 86,282)( 87,283)
( 88,284)( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)
( 96,292)( 97,293)( 98,294)( 99,344)(100,345)(101,346)(102,347)(103,348)
(104,349)(105,350)(106,351)(107,352)(108,353)(109,354)(110,355)(111,356)
(112,357)(113,358)(114,359)(115,360)(116,361)(117,362)(118,363)(119,364)
(120,365)(121,366)(122,367)(123,368)(124,369)(125,370)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,376)(132,377)(133,378)(134,379)(135,380)
(136,381)(137,382)(138,383)(139,384)(140,385)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,391)(147,392)(148,295)(149,296)(150,297)(151,298)
(152,299)(153,300)(154,301)(155,302)(156,303)(157,304)(158,305)(159,306)
(160,307)(161,308)(162,309)(163,310)(164,311)(165,312)(166,313)(167,314)
(168,315)(169,316)(170,317)(171,318)(172,319)(173,320)(174,321)(175,322)
(176,323)(177,324)(178,325)(179,326)(180,327)(181,328)(182,329)(183,330)
(184,331)(185,332)(186,333)(187,334)(188,335)(189,336)(190,337)(191,338)
(192,339)(193,340)(194,341)(195,342)(196,343);
poly := sub<Sym(392)|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 >; 
 
References : None.
to this polytope