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Polytope of Type {116,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {116,6}*1392a
Also Known As : {116,6|2}. if this polytope has another name.
Group : SmallGroup(1392,131)
Rank : 3
Schlafli Type : {116,6}
Number of vertices, edges, etc : 116, 348, 6
Order of s0s1s2 : 348
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 : {58,6}*696
   3-fold quotients : {116,2}*464
   6-fold quotients : {58,2}*232
   12-fold quotients : {29,2}*116
   29-fold quotients : {4,6}*48a
   58-fold quotients : {2,6}*24
   87-fold quotients : {4,2}*16
   116-fold quotients : {2,3}*12
   174-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)( 32, 57)
( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)( 40, 49)
( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)( 63, 84)
( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 76)
( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)( 94,111)
( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)(102,103)
(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)
(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(147,174)(148,173)
(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(155,166)(156,165)
(157,164)(158,163)(159,162)(160,161)(175,262)(176,290)(177,289)(178,288)
(179,287)(180,286)(181,285)(182,284)(183,283)(184,282)(185,281)(186,280)
(187,279)(188,278)(189,277)(190,276)(191,275)(192,274)(193,273)(194,272)
(195,271)(196,270)(197,269)(198,268)(199,267)(200,266)(201,265)(202,264)
(203,263)(204,291)(205,319)(206,318)(207,317)(208,316)(209,315)(210,314)
(211,313)(212,312)(213,311)(214,310)(215,309)(216,308)(217,307)(218,306)
(219,305)(220,304)(221,303)(222,302)(223,301)(224,300)(225,299)(226,298)
(227,297)(228,296)(229,295)(230,294)(231,293)(232,292)(233,320)(234,348)
(235,347)(236,346)(237,345)(238,344)(239,343)(240,342)(241,341)(242,340)
(243,339)(244,338)(245,337)(246,336)(247,335)(248,334)(249,333)(250,332)
(251,331)(252,330)(253,329)(254,328)(255,327)(256,326)(257,325)(258,324)
(259,323)(260,322)(261,321);;
s1 := (  1,176)(  2,175)(  3,203)(  4,202)(  5,201)(  6,200)(  7,199)(  8,198)
(  9,197)( 10,196)( 11,195)( 12,194)( 13,193)( 14,192)( 15,191)( 16,190)
( 17,189)( 18,188)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)( 24,182)
( 25,181)( 26,180)( 27,179)( 28,178)( 29,177)( 30,234)( 31,233)( 32,261)
( 33,260)( 34,259)( 35,258)( 36,257)( 37,256)( 38,255)( 39,254)( 40,253)
( 41,252)( 42,251)( 43,250)( 44,249)( 45,248)( 46,247)( 47,246)( 48,245)
( 49,244)( 50,243)( 51,242)( 52,241)( 53,240)( 54,239)( 55,238)( 56,237)
( 57,236)( 58,235)( 59,205)( 60,204)( 61,232)( 62,231)( 63,230)( 64,229)
( 65,228)( 66,227)( 67,226)( 68,225)( 69,224)( 70,223)( 71,222)( 72,221)
( 73,220)( 74,219)( 75,218)( 76,217)( 77,216)( 78,215)( 79,214)( 80,213)
( 81,212)( 82,211)( 83,210)( 84,209)( 85,208)( 86,207)( 87,206)( 88,263)
( 89,262)( 90,290)( 91,289)( 92,288)( 93,287)( 94,286)( 95,285)( 96,284)
( 97,283)( 98,282)( 99,281)(100,280)(101,279)(102,278)(103,277)(104,276)
(105,275)(106,274)(107,273)(108,272)(109,271)(110,270)(111,269)(112,268)
(113,267)(114,266)(115,265)(116,264)(117,321)(118,320)(119,348)(120,347)
(121,346)(122,345)(123,344)(124,343)(125,342)(126,341)(127,340)(128,339)
(129,338)(130,337)(131,336)(132,335)(133,334)(134,333)(135,332)(136,331)
(137,330)(138,329)(139,328)(140,327)(141,326)(142,325)(143,324)(144,323)
(145,322)(146,292)(147,291)(148,319)(149,318)(150,317)(151,316)(152,315)
(153,314)(154,313)(155,312)(156,311)(157,310)(158,309)(159,308)(160,307)
(161,306)(162,305)(163,304)(164,303)(165,302)(166,301)(167,300)(168,299)
(169,298)(170,297)(171,296)(172,295)(173,294)(174,293);;
s2 := (  1, 30)(  2, 31)(  3, 32)(  4, 33)(  5, 34)(  6, 35)(  7, 36)(  8, 37)
(  9, 38)( 10, 39)( 11, 40)( 12, 41)( 13, 42)( 14, 43)( 15, 44)( 16, 45)
( 17, 46)( 18, 47)( 19, 48)( 20, 49)( 21, 50)( 22, 51)( 23, 52)( 24, 53)
( 25, 54)( 26, 55)( 27, 56)( 28, 57)( 29, 58)( 88,117)( 89,118)( 90,119)
( 91,120)( 92,121)( 93,122)( 94,123)( 95,124)( 96,125)( 97,126)( 98,127)
( 99,128)(100,129)(101,130)(102,131)(103,132)(104,133)(105,134)(106,135)
(107,136)(108,137)(109,138)(110,139)(111,140)(112,141)(113,142)(114,143)
(115,144)(116,145)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)
(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)(188,217)
(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)(196,225)
(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232)(262,291)
(263,292)(264,293)(265,294)(266,295)(267,296)(268,297)(269,298)(270,299)
(271,300)(272,301)(273,302)(274,303)(275,304)(276,305)(277,306)(278,307)
(279,308)(280,309)(281,310)(282,311)(283,312)(284,313)(285,314)(286,315)
(287,316)(288,317)(289,318)(290,319);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(348)!(  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)
(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 31, 58)
( 32, 57)( 33, 56)( 34, 55)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 50)
( 40, 49)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 60, 87)( 61, 86)( 62, 85)
( 63, 84)( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)
( 71, 76)( 72, 75)( 73, 74)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)
( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)
(102,103)(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)
(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(147,174)
(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(155,166)
(156,165)(157,164)(158,163)(159,162)(160,161)(175,262)(176,290)(177,289)
(178,288)(179,287)(180,286)(181,285)(182,284)(183,283)(184,282)(185,281)
(186,280)(187,279)(188,278)(189,277)(190,276)(191,275)(192,274)(193,273)
(194,272)(195,271)(196,270)(197,269)(198,268)(199,267)(200,266)(201,265)
(202,264)(203,263)(204,291)(205,319)(206,318)(207,317)(208,316)(209,315)
(210,314)(211,313)(212,312)(213,311)(214,310)(215,309)(216,308)(217,307)
(218,306)(219,305)(220,304)(221,303)(222,302)(223,301)(224,300)(225,299)
(226,298)(227,297)(228,296)(229,295)(230,294)(231,293)(232,292)(233,320)
(234,348)(235,347)(236,346)(237,345)(238,344)(239,343)(240,342)(241,341)
(242,340)(243,339)(244,338)(245,337)(246,336)(247,335)(248,334)(249,333)
(250,332)(251,331)(252,330)(253,329)(254,328)(255,327)(256,326)(257,325)
(258,324)(259,323)(260,322)(261,321);
s1 := Sym(348)!(  1,176)(  2,175)(  3,203)(  4,202)(  5,201)(  6,200)(  7,199)
(  8,198)(  9,197)( 10,196)( 11,195)( 12,194)( 13,193)( 14,192)( 15,191)
( 16,190)( 17,189)( 18,188)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)
( 24,182)( 25,181)( 26,180)( 27,179)( 28,178)( 29,177)( 30,234)( 31,233)
( 32,261)( 33,260)( 34,259)( 35,258)( 36,257)( 37,256)( 38,255)( 39,254)
( 40,253)( 41,252)( 42,251)( 43,250)( 44,249)( 45,248)( 46,247)( 47,246)
( 48,245)( 49,244)( 50,243)( 51,242)( 52,241)( 53,240)( 54,239)( 55,238)
( 56,237)( 57,236)( 58,235)( 59,205)( 60,204)( 61,232)( 62,231)( 63,230)
( 64,229)( 65,228)( 66,227)( 67,226)( 68,225)( 69,224)( 70,223)( 71,222)
( 72,221)( 73,220)( 74,219)( 75,218)( 76,217)( 77,216)( 78,215)( 79,214)
( 80,213)( 81,212)( 82,211)( 83,210)( 84,209)( 85,208)( 86,207)( 87,206)
( 88,263)( 89,262)( 90,290)( 91,289)( 92,288)( 93,287)( 94,286)( 95,285)
( 96,284)( 97,283)( 98,282)( 99,281)(100,280)(101,279)(102,278)(103,277)
(104,276)(105,275)(106,274)(107,273)(108,272)(109,271)(110,270)(111,269)
(112,268)(113,267)(114,266)(115,265)(116,264)(117,321)(118,320)(119,348)
(120,347)(121,346)(122,345)(123,344)(124,343)(125,342)(126,341)(127,340)
(128,339)(129,338)(130,337)(131,336)(132,335)(133,334)(134,333)(135,332)
(136,331)(137,330)(138,329)(139,328)(140,327)(141,326)(142,325)(143,324)
(144,323)(145,322)(146,292)(147,291)(148,319)(149,318)(150,317)(151,316)
(152,315)(153,314)(154,313)(155,312)(156,311)(157,310)(158,309)(159,308)
(160,307)(161,306)(162,305)(163,304)(164,303)(165,302)(166,301)(167,300)
(168,299)(169,298)(170,297)(171,296)(172,295)(173,294)(174,293);
s2 := Sym(348)!(  1, 30)(  2, 31)(  3, 32)(  4, 33)(  5, 34)(  6, 35)(  7, 36)
(  8, 37)(  9, 38)( 10, 39)( 11, 40)( 12, 41)( 13, 42)( 14, 43)( 15, 44)
( 16, 45)( 17, 46)( 18, 47)( 19, 48)( 20, 49)( 21, 50)( 22, 51)( 23, 52)
( 24, 53)( 25, 54)( 26, 55)( 27, 56)( 28, 57)( 29, 58)( 88,117)( 89,118)
( 90,119)( 91,120)( 92,121)( 93,122)( 94,123)( 95,124)( 96,125)( 97,126)
( 98,127)( 99,128)(100,129)(101,130)(102,131)(103,132)(104,133)(105,134)
(106,135)(107,136)(108,137)(109,138)(110,139)(111,140)(112,141)(113,142)
(114,143)(115,144)(116,145)(175,204)(176,205)(177,206)(178,207)(179,208)
(180,209)(181,210)(182,211)(183,212)(184,213)(185,214)(186,215)(187,216)
(188,217)(189,218)(190,219)(191,220)(192,221)(193,222)(194,223)(195,224)
(196,225)(197,226)(198,227)(199,228)(200,229)(201,230)(202,231)(203,232)
(262,291)(263,292)(264,293)(265,294)(266,295)(267,296)(268,297)(269,298)
(270,299)(271,300)(272,301)(273,302)(274,303)(275,304)(276,305)(277,306)
(278,307)(279,308)(280,309)(281,310)(282,311)(283,312)(284,313)(285,314)
(286,315)(287,316)(288,317)(289,318)(290,319);
poly := sub<Sym(348)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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