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