Polytope of Type {2,352}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,352}*1408
if this polytope has a name.
Group : SmallGroup(1408,6808)
Rank : 3
Schlafli Type : {2,352}
Number of vertices, edges, etc : 2, 352, 352
Order of s₀s₁s₂ : 352
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 : {2,176}*704
   4-fold quotients : {2,88}*352
   8-fold quotients : {2,44}*176
   11-fold quotients : {2,32}*128
   16-fold quotients : {2,22}*88
   22-fold quotients : {2,16}*64
   32-fold quotients : {2,11}*44
   44-fold quotients : {2,8}*32
   88-fold quotients : {2,4}*16
   176-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.

Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 69)( 48, 79)( 49, 78)( 50, 77)( 51, 76)( 52, 75)( 53, 74)( 54, 73)( 55, 72)( 56, 71)( 57, 70)( 58, 80)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 91,135)( 92,145)( 93,144)( 94,143)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,146)(103,156)(104,155)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,157)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(179,267)(180,277)(181,276)(182,275)(183,274)(184,273)(185,272)(186,271)(187,270)(188,269)(189,268)(190,278)(191,288)(192,287)(193,286)(194,285)(195,284)(196,283)(197,282)(198,281)(199,280)(200,279)(201,300)(202,310)(203,309)(204,308)(205,307)(206,306)(207,305)(208,304)(209,303)(210,302)(211,301)(212,289)(213,299)(214,298)(215,297)(216,296)(217,295)(218,294)(219,293)(220,292)(221,291)(222,290)(223,333)(224,343)(225,342)(226,341)(227,340)(228,339)(229,338)(230,337)(231,336)(232,335)(233,334)(234,344)(235,354)(236,353)(237,352)(238,351)(239,350)(240,349)(241,348)(242,347)(243,346)(244,345)(245,311)(246,321)(247,320)(248,319)(249,318)(250,317)(251,316)(252,315)(253,314)(254,313)(255,312)(256,322)(257,332)(258,331)(259,330)(260,329)(261,328)(262,327)(263,326)(264,325)(265,324)(266,323);;
s2 := (  3,180)(  4,179)(  5,189)(  6,188)(  7,187)(  8,186)(  9,185)( 10,184)( 11,183)( 12,182)( 13,181)( 14,191)( 15,190)( 16,200)( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)( 24,192)( 25,213)( 26,212)( 27,222)( 28,221)( 29,220)( 30,219)( 31,218)( 32,217)( 33,216)( 34,215)( 35,214)( 36,202)( 37,201)( 38,211)( 39,210)( 40,209)( 41,208)( 42,207)( 43,206)( 44,205)( 45,204)( 46,203)( 47,246)( 48,245)( 49,255)( 50,254)( 51,253)( 52,252)( 53,251)( 54,250)( 55,249)( 56,248)( 57,247)( 58,257)( 59,256)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)( 65,261)( 66,260)( 67,259)( 68,258)( 69,224)( 70,223)( 71,233)( 72,232)( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,226)( 79,225)( 80,235)( 81,234)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)( 89,237)( 90,236)( 91,312)( 92,311)( 93,321)( 94,320)( 95,319)( 96,318)( 97,317)( 98,316)( 99,315)(100,314)(101,313)(102,323)(103,322)(104,332)(105,331)(106,330)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)(113,345)(114,344)(115,354)(116,353)(117,352)(118,351)(119,350)(120,349)(121,348)(122,347)(123,346)(124,334)(125,333)(126,343)(127,342)(128,341)(129,340)(130,339)(131,338)(132,337)(133,336)(134,335)(135,268)(136,267)(137,277)(138,276)(139,275)(140,274)(141,273)(142,272)(143,271)(144,270)(145,269)(146,279)(147,278)(148,288)(149,287)(150,286)(151,285)(152,284)(153,283)(154,282)(155,281)(156,280)(157,301)(158,300)(159,310)(160,309)(161,308)(162,307)(163,306)(164,305)(165,304)(166,303)(167,302)(168,290)(169,289)(170,299)(171,298)(172,297)(173,296)(174,295)(175,294)(176,293)(177,292)(178,291);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(354)!(1,2);
s1 := Sym(354)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 69)( 48, 79)( 49, 78)( 50, 77)( 51, 76)( 52, 75)( 53, 74)( 54, 73)( 55, 72)( 56, 71)( 57, 70)( 58, 80)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 91,135)( 92,145)( 93,144)( 94,143)( 95,142)( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,146)(103,156)(104,155)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,157)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(179,267)(180,277)(181,276)(182,275)(183,274)(184,273)(185,272)(186,271)(187,270)(188,269)(189,268)(190,278)(191,288)(192,287)(193,286)(194,285)(195,284)(196,283)(197,282)(198,281)(199,280)(200,279)(201,300)(202,310)(203,309)(204,308)(205,307)(206,306)(207,305)(208,304)(209,303)(210,302)(211,301)(212,289)(213,299)(214,298)(215,297)(216,296)(217,295)(218,294)(219,293)(220,292)(221,291)(222,290)(223,333)(224,343)(225,342)(226,341)(227,340)(228,339)(229,338)(230,337)(231,336)(232,335)(233,334)(234,344)(235,354)(236,353)(237,352)(238,351)(239,350)(240,349)(241,348)(242,347)(243,346)(244,345)(245,311)(246,321)(247,320)(248,319)(249,318)(250,317)(251,316)(252,315)(253,314)(254,313)(255,312)(256,322)(257,332)(258,331)(259,330)(260,329)(261,328)(262,327)(263,326)(264,325)(265,324)(266,323);
s2 := Sym(354)!(  3,180)(  4,179)(  5,189)(  6,188)(  7,187)(  8,186)(  9,185)( 10,184)( 11,183)( 12,182)( 13,181)( 14,191)( 15,190)( 16,200)( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)( 24,192)( 25,213)( 26,212)( 27,222)( 28,221)( 29,220)( 30,219)( 31,218)( 32,217)( 33,216)( 34,215)( 35,214)( 36,202)( 37,201)( 38,211)( 39,210)( 40,209)( 41,208)( 42,207)( 43,206)( 44,205)( 45,204)( 46,203)( 47,246)( 48,245)( 49,255)( 50,254)( 51,253)( 52,252)( 53,251)( 54,250)( 55,249)( 56,248)( 57,247)( 58,257)( 59,256)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)( 65,261)( 66,260)( 67,259)( 68,258)( 69,224)( 70,223)( 71,233)( 72,232)( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,226)( 79,225)( 80,235)( 81,234)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)( 89,237)( 90,236)( 91,312)( 92,311)( 93,321)( 94,320)( 95,319)( 96,318)( 97,317)( 98,316)( 99,315)(100,314)(101,313)(102,323)(103,322)(104,332)(105,331)(106,330)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)(113,345)(114,344)(115,354)(116,353)(117,352)(118,351)(119,350)(120,349)(121,348)(122,347)(123,346)(124,334)(125,333)(126,343)(127,342)(128,341)(129,340)(130,339)(131,338)(132,337)(133,336)(134,335)(135,268)(136,267)(137,277)(138,276)(139,275)(140,274)(141,273)(142,272)(143,271)(144,270)(145,269)(146,279)(147,278)(148,288)(149,287)(150,286)(151,285)(152,284)(153,283)(154,282)(155,281)(156,280)(157,301)(158,300)(159,310)(160,309)(161,308)(162,307)(163,306)(164,305)(165,304)(166,303)(167,302)(168,290)(169,289)(170,299)(171,298)(172,297)(173,296)(174,295)(175,294)(176,293)(177,292)(178,291);
poly := sub<Sym(354)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope