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