Polytope of Type {2,368}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,368}*1472
if this polytope has a name.
Group : SmallGroup(1472,970)
Rank : 3
Schlafli Type : {2,368}
Number of vertices, edges, etc : 2, 368, 368
Order of s₀s₁s₂ : 368
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 : {2,184}*736
   4-fold quotients : {2,92}*368
   8-fold quotients : {2,46}*184
   16-fold quotients : {2,23}*92
   23-fold quotients : {2,16}*64
   46-fold quotients : {2,8}*32
   92-fold quotients : {2,4}*16
   184-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)
( 12, 17)( 13, 16)( 14, 15)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)
( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 49, 72)( 50, 94)
( 51, 93)( 52, 92)( 53, 91)( 54, 90)( 55, 89)( 56, 88)( 57, 87)( 58, 86)
( 59, 85)( 60, 84)( 61, 83)( 62, 82)( 63, 81)( 64, 80)( 65, 79)( 66, 78)
( 67, 77)( 68, 76)( 69, 75)( 70, 74)( 71, 73)( 95,141)( 96,163)( 97,162)
( 98,161)( 99,160)(100,159)(101,158)(102,157)(103,156)(104,155)(105,154)
(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,146)
(114,145)(115,144)(116,143)(117,142)(118,164)(119,186)(120,185)(121,184)
(122,183)(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)
(130,175)(131,174)(132,173)(133,172)(134,171)(135,170)(136,169)(137,168)
(138,167)(139,166)(140,165)(187,279)(188,301)(189,300)(190,299)(191,298)
(192,297)(193,296)(194,295)(195,294)(196,293)(197,292)(198,291)(199,290)
(200,289)(201,288)(202,287)(203,286)(204,285)(205,284)(206,283)(207,282)
(208,281)(209,280)(210,302)(211,324)(212,323)(213,322)(214,321)(215,320)
(216,319)(217,318)(218,317)(219,316)(220,315)(221,314)(222,313)(223,312)
(224,311)(225,310)(226,309)(227,308)(228,307)(229,306)(230,305)(231,304)
(232,303)(233,348)(234,370)(235,369)(236,368)(237,367)(238,366)(239,365)
(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,358)(247,357)
(248,356)(249,355)(250,354)(251,353)(252,352)(253,351)(254,350)(255,349)
(256,325)(257,347)(258,346)(259,345)(260,344)(261,343)(262,342)(263,341)
(264,340)(265,339)(266,338)(267,337)(268,336)(269,335)(270,334)(271,333)
(272,332)(273,331)(274,330)(275,329)(276,328)(277,327)(278,326);;
s2 := (  3,188)(  4,187)(  5,209)(  6,208)(  7,207)(  8,206)(  9,205)( 10,204)
( 11,203)( 12,202)( 13,201)( 14,200)( 15,199)( 16,198)( 17,197)( 18,196)
( 19,195)( 20,194)( 21,193)( 22,192)( 23,191)( 24,190)( 25,189)( 26,211)
( 27,210)( 28,232)( 29,231)( 30,230)( 31,229)( 32,228)( 33,227)( 34,226)
( 35,225)( 36,224)( 37,223)( 38,222)( 39,221)( 40,220)( 41,219)( 42,218)
( 43,217)( 44,216)( 45,215)( 46,214)( 47,213)( 48,212)( 49,257)( 50,256)
( 51,278)( 52,277)( 53,276)( 54,275)( 55,274)( 56,273)( 57,272)( 58,271)
( 59,270)( 60,269)( 61,268)( 62,267)( 63,266)( 64,265)( 65,264)( 66,263)
( 67,262)( 68,261)( 69,260)( 70,259)( 71,258)( 72,234)( 73,233)( 74,255)
( 75,254)( 76,253)( 77,252)( 78,251)( 79,250)( 80,249)( 81,248)( 82,247)
( 83,246)( 84,245)( 85,244)( 86,243)( 87,242)( 88,241)( 89,240)( 90,239)
( 91,238)( 92,237)( 93,236)( 94,235)( 95,326)( 96,325)( 97,347)( 98,346)
( 99,345)(100,344)(101,343)(102,342)(103,341)(104,340)(105,339)(106,338)
(107,337)(108,336)(109,335)(110,334)(111,333)(112,332)(113,331)(114,330)
(115,329)(116,328)(117,327)(118,349)(119,348)(120,370)(121,369)(122,368)
(123,367)(124,366)(125,365)(126,364)(127,363)(128,362)(129,361)(130,360)
(131,359)(132,358)(133,357)(134,356)(135,355)(136,354)(137,353)(138,352)
(139,351)(140,350)(141,280)(142,279)(143,301)(144,300)(145,299)(146,298)
(147,297)(148,296)(149,295)(150,294)(151,293)(152,292)(153,291)(154,290)
(155,289)(156,288)(157,287)(158,286)(159,285)(160,284)(161,283)(162,282)
(163,281)(164,303)(165,302)(166,324)(167,323)(168,322)(169,321)(170,320)
(171,319)(172,318)(173,317)(174,316)(175,315)(176,314)(177,313)(178,312)
(179,311)(180,310)(181,309)(182,308)(183,307)(184,306)(185,305)(186,304);;
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*s1*s2*s1*s2*s1*s2*s1*s2*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(370)!(1,2);
s1 := Sym(370)!(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)
( 11, 18)( 12, 17)( 13, 16)( 14, 15)( 27, 48)( 28, 47)( 29, 46)( 30, 45)
( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 49, 72)
( 50, 94)( 51, 93)( 52, 92)( 53, 91)( 54, 90)( 55, 89)( 56, 88)( 57, 87)
( 58, 86)( 59, 85)( 60, 84)( 61, 83)( 62, 82)( 63, 81)( 64, 80)( 65, 79)
( 66, 78)( 67, 77)( 68, 76)( 69, 75)( 70, 74)( 71, 73)( 95,141)( 96,163)
( 97,162)( 98,161)( 99,160)(100,159)(101,158)(102,157)(103,156)(104,155)
(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)
(113,146)(114,145)(115,144)(116,143)(117,142)(118,164)(119,186)(120,185)
(121,184)(122,183)(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)
(129,176)(130,175)(131,174)(132,173)(133,172)(134,171)(135,170)(136,169)
(137,168)(138,167)(139,166)(140,165)(187,279)(188,301)(189,300)(190,299)
(191,298)(192,297)(193,296)(194,295)(195,294)(196,293)(197,292)(198,291)
(199,290)(200,289)(201,288)(202,287)(203,286)(204,285)(205,284)(206,283)
(207,282)(208,281)(209,280)(210,302)(211,324)(212,323)(213,322)(214,321)
(215,320)(216,319)(217,318)(218,317)(219,316)(220,315)(221,314)(222,313)
(223,312)(224,311)(225,310)(226,309)(227,308)(228,307)(229,306)(230,305)
(231,304)(232,303)(233,348)(234,370)(235,369)(236,368)(237,367)(238,366)
(239,365)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,358)
(247,357)(248,356)(249,355)(250,354)(251,353)(252,352)(253,351)(254,350)
(255,349)(256,325)(257,347)(258,346)(259,345)(260,344)(261,343)(262,342)
(263,341)(264,340)(265,339)(266,338)(267,337)(268,336)(269,335)(270,334)
(271,333)(272,332)(273,331)(274,330)(275,329)(276,328)(277,327)(278,326);
s2 := Sym(370)!(  3,188)(  4,187)(  5,209)(  6,208)(  7,207)(  8,206)(  9,205)
( 10,204)( 11,203)( 12,202)( 13,201)( 14,200)( 15,199)( 16,198)( 17,197)
( 18,196)( 19,195)( 20,194)( 21,193)( 22,192)( 23,191)( 24,190)( 25,189)
( 26,211)( 27,210)( 28,232)( 29,231)( 30,230)( 31,229)( 32,228)( 33,227)
( 34,226)( 35,225)( 36,224)( 37,223)( 38,222)( 39,221)( 40,220)( 41,219)
( 42,218)( 43,217)( 44,216)( 45,215)( 46,214)( 47,213)( 48,212)( 49,257)
( 50,256)( 51,278)( 52,277)( 53,276)( 54,275)( 55,274)( 56,273)( 57,272)
( 58,271)( 59,270)( 60,269)( 61,268)( 62,267)( 63,266)( 64,265)( 65,264)
( 66,263)( 67,262)( 68,261)( 69,260)( 70,259)( 71,258)( 72,234)( 73,233)
( 74,255)( 75,254)( 76,253)( 77,252)( 78,251)( 79,250)( 80,249)( 81,248)
( 82,247)( 83,246)( 84,245)( 85,244)( 86,243)( 87,242)( 88,241)( 89,240)
( 90,239)( 91,238)( 92,237)( 93,236)( 94,235)( 95,326)( 96,325)( 97,347)
( 98,346)( 99,345)(100,344)(101,343)(102,342)(103,341)(104,340)(105,339)
(106,338)(107,337)(108,336)(109,335)(110,334)(111,333)(112,332)(113,331)
(114,330)(115,329)(116,328)(117,327)(118,349)(119,348)(120,370)(121,369)
(122,368)(123,367)(124,366)(125,365)(126,364)(127,363)(128,362)(129,361)
(130,360)(131,359)(132,358)(133,357)(134,356)(135,355)(136,354)(137,353)
(138,352)(139,351)(140,350)(141,280)(142,279)(143,301)(144,300)(145,299)
(146,298)(147,297)(148,296)(149,295)(150,294)(151,293)(152,292)(153,291)
(154,290)(155,289)(156,288)(157,287)(158,286)(159,285)(160,284)(161,283)
(162,282)(163,281)(164,303)(165,302)(166,324)(167,323)(168,322)(169,321)
(170,320)(171,319)(172,318)(173,317)(174,316)(175,315)(176,314)(177,313)
(178,312)(179,311)(180,310)(181,309)(182,308)(183,307)(184,306)(185,305)
(186,304);
poly := sub<Sym(370)|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*s1*s2*s1*s2*s1*s2*s1*s2*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