Polytope of Type {2,348}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,348}*1392
if this polytope has a name.
Group : SmallGroup(1392,171)
Rank : 3
Schlafli Type : {2,348}
Number of vertices, edges, etc : 2, 348, 348
Order of s₀s₁s₂ : 348
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,174}*696
   3-fold quotients : {2,116}*464
   4-fold quotients : {2,87}*348
   6-fold quotients : {2,58}*232
   12-fold quotients : {2,29}*116
   29-fold quotients : {2,12}*48
   58-fold quotients : {2,6}*24
   87-fold quotients : {2,4}*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 := (1,2);;
s1 := (  4, 31)(  5, 30)(  6, 29)(  7, 28)(  8, 27)(  9, 26)( 10, 25)( 11, 24)
( 12, 23)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 32, 61)( 33, 89)
( 34, 88)( 35, 87)( 36, 86)( 37, 85)( 38, 84)( 39, 83)( 40, 82)( 41, 81)
( 42, 80)( 43, 79)( 44, 78)( 45, 77)( 46, 76)( 47, 75)( 48, 74)( 49, 73)
( 50, 72)( 51, 71)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 66)( 57, 65)
( 58, 64)( 59, 63)( 60, 62)( 91,118)( 92,117)( 93,116)( 94,115)( 95,114)
( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)
(104,105)(119,148)(120,176)(121,175)(122,174)(123,173)(124,172)(125,171)
(126,170)(127,169)(128,168)(129,167)(130,166)(131,165)(132,164)(133,163)
(134,162)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)(141,155)
(142,154)(143,153)(144,152)(145,151)(146,150)(147,149)(177,264)(178,292)
(179,291)(180,290)(181,289)(182,288)(183,287)(184,286)(185,285)(186,284)
(187,283)(188,282)(189,281)(190,280)(191,279)(192,278)(193,277)(194,276)
(195,275)(196,274)(197,273)(198,272)(199,271)(200,270)(201,269)(202,268)
(203,267)(204,266)(205,265)(206,322)(207,350)(208,349)(209,348)(210,347)
(211,346)(212,345)(213,344)(214,343)(215,342)(216,341)(217,340)(218,339)
(219,338)(220,337)(221,336)(222,335)(223,334)(224,333)(225,332)(226,331)
(227,330)(228,329)(229,328)(230,327)(231,326)(232,325)(233,324)(234,323)
(235,293)(236,321)(237,320)(238,319)(239,318)(240,317)(241,316)(242,315)
(243,314)(244,313)(245,312)(246,311)(247,310)(248,309)(249,308)(250,307)
(251,306)(252,305)(253,304)(254,303)(255,302)(256,301)(257,300)(258,299)
(259,298)(260,297)(261,296)(262,295)(263,294);;
s2 := (  3,207)(  4,206)(  5,234)(  6,233)(  7,232)(  8,231)(  9,230)( 10,229)
( 11,228)( 12,227)( 13,226)( 14,225)( 15,224)( 16,223)( 17,222)( 18,221)
( 19,220)( 20,219)( 21,218)( 22,217)( 23,216)( 24,215)( 25,214)( 26,213)
( 27,212)( 28,211)( 29,210)( 30,209)( 31,208)( 32,178)( 33,177)( 34,205)
( 35,204)( 36,203)( 37,202)( 38,201)( 39,200)( 40,199)( 41,198)( 42,197)
( 43,196)( 44,195)( 45,194)( 46,193)( 47,192)( 48,191)( 49,190)( 50,189)
( 51,188)( 52,187)( 53,186)( 54,185)( 55,184)( 56,183)( 57,182)( 58,181)
( 59,180)( 60,179)( 61,236)( 62,235)( 63,263)( 64,262)( 65,261)( 66,260)
( 67,259)( 68,258)( 69,257)( 70,256)( 71,255)( 72,254)( 73,253)( 74,252)
( 75,251)( 76,250)( 77,249)( 78,248)( 79,247)( 80,246)( 81,245)( 82,244)
( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)( 89,237)( 90,294)
( 91,293)( 92,321)( 93,320)( 94,319)( 95,318)( 96,317)( 97,316)( 98,315)
( 99,314)(100,313)(101,312)(102,311)(103,310)(104,309)(105,308)(106,307)
(107,306)(108,305)(109,304)(110,303)(111,302)(112,301)(113,300)(114,299)
(115,298)(116,297)(117,296)(118,295)(119,265)(120,264)(121,292)(122,291)
(123,290)(124,289)(125,288)(126,287)(127,286)(128,285)(129,284)(130,283)
(131,282)(132,281)(133,280)(134,279)(135,278)(136,277)(137,276)(138,275)
(139,274)(140,273)(141,272)(142,271)(143,270)(144,269)(145,268)(146,267)
(147,266)(148,323)(149,322)(150,350)(151,349)(152,348)(153,347)(154,346)
(155,345)(156,344)(157,343)(158,342)(159,341)(160,340)(161,339)(162,338)
(163,337)(164,336)(165,335)(166,334)(167,333)(168,332)(169,331)(170,330)
(171,329)(172,328)(173,327)(174,326)(175,325)(176,324);;
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*s1*s0*s1, s0*s2*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*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*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*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*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(350)!(1,2);
s1 := Sym(350)!(  4, 31)(  5, 30)(  6, 29)(  7, 28)(  8, 27)(  9, 26)( 10, 25)
( 11, 24)( 12, 23)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 32, 61)
( 33, 89)( 34, 88)( 35, 87)( 36, 86)( 37, 85)( 38, 84)( 39, 83)( 40, 82)
( 41, 81)( 42, 80)( 43, 79)( 44, 78)( 45, 77)( 46, 76)( 47, 75)( 48, 74)
( 49, 73)( 50, 72)( 51, 71)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 66)
( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 91,118)( 92,117)( 93,116)( 94,115)
( 95,114)( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)
(103,106)(104,105)(119,148)(120,176)(121,175)(122,174)(123,173)(124,172)
(125,171)(126,170)(127,169)(128,168)(129,167)(130,166)(131,165)(132,164)
(133,163)(134,162)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)
(141,155)(142,154)(143,153)(144,152)(145,151)(146,150)(147,149)(177,264)
(178,292)(179,291)(180,290)(181,289)(182,288)(183,287)(184,286)(185,285)
(186,284)(187,283)(188,282)(189,281)(190,280)(191,279)(192,278)(193,277)
(194,276)(195,275)(196,274)(197,273)(198,272)(199,271)(200,270)(201,269)
(202,268)(203,267)(204,266)(205,265)(206,322)(207,350)(208,349)(209,348)
(210,347)(211,346)(212,345)(213,344)(214,343)(215,342)(216,341)(217,340)
(218,339)(219,338)(220,337)(221,336)(222,335)(223,334)(224,333)(225,332)
(226,331)(227,330)(228,329)(229,328)(230,327)(231,326)(232,325)(233,324)
(234,323)(235,293)(236,321)(237,320)(238,319)(239,318)(240,317)(241,316)
(242,315)(243,314)(244,313)(245,312)(246,311)(247,310)(248,309)(249,308)
(250,307)(251,306)(252,305)(253,304)(254,303)(255,302)(256,301)(257,300)
(258,299)(259,298)(260,297)(261,296)(262,295)(263,294);
s2 := Sym(350)!(  3,207)(  4,206)(  5,234)(  6,233)(  7,232)(  8,231)(  9,230)
( 10,229)( 11,228)( 12,227)( 13,226)( 14,225)( 15,224)( 16,223)( 17,222)
( 18,221)( 19,220)( 20,219)( 21,218)( 22,217)( 23,216)( 24,215)( 25,214)
( 26,213)( 27,212)( 28,211)( 29,210)( 30,209)( 31,208)( 32,178)( 33,177)
( 34,205)( 35,204)( 36,203)( 37,202)( 38,201)( 39,200)( 40,199)( 41,198)
( 42,197)( 43,196)( 44,195)( 45,194)( 46,193)( 47,192)( 48,191)( 49,190)
( 50,189)( 51,188)( 52,187)( 53,186)( 54,185)( 55,184)( 56,183)( 57,182)
( 58,181)( 59,180)( 60,179)( 61,236)( 62,235)( 63,263)( 64,262)( 65,261)
( 66,260)( 67,259)( 68,258)( 69,257)( 70,256)( 71,255)( 72,254)( 73,253)
( 74,252)( 75,251)( 76,250)( 77,249)( 78,248)( 79,247)( 80,246)( 81,245)
( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)( 89,237)
( 90,294)( 91,293)( 92,321)( 93,320)( 94,319)( 95,318)( 96,317)( 97,316)
( 98,315)( 99,314)(100,313)(101,312)(102,311)(103,310)(104,309)(105,308)
(106,307)(107,306)(108,305)(109,304)(110,303)(111,302)(112,301)(113,300)
(114,299)(115,298)(116,297)(117,296)(118,295)(119,265)(120,264)(121,292)
(122,291)(123,290)(124,289)(125,288)(126,287)(127,286)(128,285)(129,284)
(130,283)(131,282)(132,281)(133,280)(134,279)(135,278)(136,277)(137,276)
(138,275)(139,274)(140,273)(141,272)(142,271)(143,270)(144,269)(145,268)
(146,267)(147,266)(148,323)(149,322)(150,350)(151,349)(152,348)(153,347)
(154,346)(155,345)(156,344)(157,343)(158,342)(159,341)(160,340)(161,339)
(162,338)(163,337)(164,336)(165,335)(166,334)(167,333)(168,332)(169,331)
(170,330)(171,329)(172,328)(173,327)(174,326)(175,325)(176,324);
poly := sub<Sym(350)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*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*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*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*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*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 >;

to this polytope