Polytope of Type {20,34}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,34}*1360
Also Known As : {20,34|2}. if this polytope has another name.
Group : SmallGroup(1360,170)
Rank : 3
Schlafli Type : {20,34}
Number of vertices, edges, etc : 20, 340, 34
Order of s0s1s2 : 340
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 : {10,34}*680
5-fold quotients : {4,34}*272
10-fold quotients : {2,34}*136
17-fold quotients : {20,2}*80
20-fold quotients : {2,17}*68
34-fold quotients : {10,2}*40
68-fold quotients : {5,2}*20
85-fold quotients : {4,2}*16
170-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 18, 69)( 19, 70)( 20, 71)( 21, 72)( 22, 73)( 23, 74)( 24, 75)( 25, 76)
( 26, 77)( 27, 78)( 28, 79)( 29, 80)( 30, 81)( 31, 82)( 32, 83)( 33, 84)
( 34, 85)( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)
( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)
( 50, 67)( 51, 68)(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)
(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)
(117,168)(118,169)(119,170)(120,137)(121,138)(122,139)(123,140)(124,141)
(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)
(133,150)(134,151)(135,152)(136,153)(171,256)(172,257)(173,258)(174,259)
(175,260)(176,261)(177,262)(178,263)(179,264)(180,265)(181,266)(182,267)
(183,268)(184,269)(185,270)(186,271)(187,272)(188,324)(189,325)(190,326)
(191,327)(192,328)(193,329)(194,330)(195,331)(196,332)(197,333)(198,334)
(199,335)(200,336)(201,337)(202,338)(203,339)(204,340)(205,307)(206,308)
(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)
(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(222,290)
(223,291)(224,292)(225,293)(226,294)(227,295)(228,296)(229,297)(230,298)
(231,299)(232,300)(233,301)(234,302)(235,303)(236,304)(237,305)(238,306)
(239,273)(240,274)(241,275)(242,276)(243,277)(244,278)(245,279)(246,280)
(247,281)(248,282)(249,283)(250,284)(251,285)(252,286)(253,287)(254,288)
(255,289);;
s1 := ( 1,188)( 2,204)( 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)( 18,171)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)( 24,182)
( 25,181)( 26,180)( 27,179)( 28,178)( 29,177)( 30,176)( 31,175)( 32,174)
( 33,173)( 34,172)( 35,239)( 36,255)( 37,254)( 38,253)( 39,252)( 40,251)
( 41,250)( 42,249)( 43,248)( 44,247)( 45,246)( 46,245)( 47,244)( 48,243)
( 49,242)( 50,241)( 51,240)( 52,222)( 53,238)( 54,237)( 55,236)( 56,235)
( 57,234)( 58,233)( 59,232)( 60,231)( 61,230)( 62,229)( 63,228)( 64,227)
( 65,226)( 66,225)( 67,224)( 68,223)( 69,205)( 70,221)( 71,220)( 72,219)
( 73,218)( 74,217)( 75,216)( 76,215)( 77,214)( 78,213)( 79,212)( 80,211)
( 81,210)( 82,209)( 83,208)( 84,207)( 85,206)( 86,273)( 87,289)( 88,288)
( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)
( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,256)(104,272)
(105,271)(106,270)(107,269)(108,268)(109,267)(110,266)(111,265)(112,264)
(113,263)(114,262)(115,261)(116,260)(117,259)(118,258)(119,257)(120,324)
(121,340)(122,339)(123,338)(124,337)(125,336)(126,335)(127,334)(128,333)
(129,332)(130,331)(131,330)(132,329)(133,328)(134,327)(135,326)(136,325)
(137,307)(138,323)(139,322)(140,321)(141,320)(142,319)(143,318)(144,317)
(145,316)(146,315)(147,314)(148,313)(149,312)(150,311)(151,310)(152,309)
(153,308)(154,290)(155,306)(156,305)(157,304)(158,303)(159,302)(160,301)
(161,300)(162,299)(163,298)(164,297)(165,296)(166,295)(167,294)(168,293)
(169,292)(170,291);;
s2 := ( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)
( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)
( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)
(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)
(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)
(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)
(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)
(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)(179,181)
(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)
(205,206)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215)
(222,223)(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)(230,232)
(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)
(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)(264,266)
(273,274)(275,289)(276,288)(277,287)(278,286)(279,285)(280,284)(281,283)
(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)
(307,308)(309,323)(310,322)(311,321)(312,320)(313,319)(314,318)(315,317)
(324,325)(326,340)(327,339)(328,338)(329,337)(330,336)(331,335)(332,334);;
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,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(340)!( 18, 69)( 19, 70)( 20, 71)( 21, 72)( 22, 73)( 23, 74)( 24, 75)
( 25, 76)( 26, 77)( 27, 78)( 28, 79)( 29, 80)( 30, 81)( 31, 82)( 32, 83)
( 33, 84)( 34, 85)( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)
( 41, 58)( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)
( 49, 66)( 50, 67)( 51, 68)(103,154)(104,155)(105,156)(106,157)(107,158)
(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)
(116,167)(117,168)(118,169)(119,170)(120,137)(121,138)(122,139)(123,140)
(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)
(132,149)(133,150)(134,151)(135,152)(136,153)(171,256)(172,257)(173,258)
(174,259)(175,260)(176,261)(177,262)(178,263)(179,264)(180,265)(181,266)
(182,267)(183,268)(184,269)(185,270)(186,271)(187,272)(188,324)(189,325)
(190,326)(191,327)(192,328)(193,329)(194,330)(195,331)(196,332)(197,333)
(198,334)(199,335)(200,336)(201,337)(202,338)(203,339)(204,340)(205,307)
(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)
(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)
(222,290)(223,291)(224,292)(225,293)(226,294)(227,295)(228,296)(229,297)
(230,298)(231,299)(232,300)(233,301)(234,302)(235,303)(236,304)(237,305)
(238,306)(239,273)(240,274)(241,275)(242,276)(243,277)(244,278)(245,279)
(246,280)(247,281)(248,282)(249,283)(250,284)(251,285)(252,286)(253,287)
(254,288)(255,289);
s1 := Sym(340)!( 1,188)( 2,204)( 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)( 18,171)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)
( 24,182)( 25,181)( 26,180)( 27,179)( 28,178)( 29,177)( 30,176)( 31,175)
( 32,174)( 33,173)( 34,172)( 35,239)( 36,255)( 37,254)( 38,253)( 39,252)
( 40,251)( 41,250)( 42,249)( 43,248)( 44,247)( 45,246)( 46,245)( 47,244)
( 48,243)( 49,242)( 50,241)( 51,240)( 52,222)( 53,238)( 54,237)( 55,236)
( 56,235)( 57,234)( 58,233)( 59,232)( 60,231)( 61,230)( 62,229)( 63,228)
( 64,227)( 65,226)( 66,225)( 67,224)( 68,223)( 69,205)( 70,221)( 71,220)
( 72,219)( 73,218)( 74,217)( 75,216)( 76,215)( 77,214)( 78,213)( 79,212)
( 80,211)( 81,210)( 82,209)( 83,208)( 84,207)( 85,206)( 86,273)( 87,289)
( 88,288)( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)
( 96,280)( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,256)
(104,272)(105,271)(106,270)(107,269)(108,268)(109,267)(110,266)(111,265)
(112,264)(113,263)(114,262)(115,261)(116,260)(117,259)(118,258)(119,257)
(120,324)(121,340)(122,339)(123,338)(124,337)(125,336)(126,335)(127,334)
(128,333)(129,332)(130,331)(131,330)(132,329)(133,328)(134,327)(135,326)
(136,325)(137,307)(138,323)(139,322)(140,321)(141,320)(142,319)(143,318)
(144,317)(145,316)(146,315)(147,314)(148,313)(149,312)(150,311)(151,310)
(152,309)(153,308)(154,290)(155,306)(156,305)(157,304)(158,303)(159,302)
(160,301)(161,300)(162,299)(163,298)(164,297)(165,296)(166,295)(167,294)
(168,293)(169,292)(170,291);
s2 := Sym(340)!( 1, 2)( 3, 17)( 4, 16)( 5, 15)( 6, 14)( 7, 13)( 8, 12)
( 9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)
( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)
( 60, 62)( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)
( 94, 96)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)
(111,113)(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)
(128,130)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)
(145,147)(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)
(162,164)(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)
(179,181)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)
(196,198)(205,206)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)
(213,215)(222,223)(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)
(230,232)(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)
(247,249)(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)
(264,266)(273,274)(275,289)(276,288)(277,287)(278,286)(279,285)(280,284)
(281,283)(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)
(298,300)(307,308)(309,323)(310,322)(311,321)(312,320)(313,319)(314,318)
(315,317)(324,325)(326,340)(327,339)(328,338)(329,337)(330,336)(331,335)
(332,334);
poly := sub<Sym(340)|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,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope