Polytope of Type {34,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34,18}*1224
Also Known As : {34,18|2}. if this polytope has another name.
Group : SmallGroup(1224,47)
Rank : 3
Schlafli Type : {34,18}
Number of vertices, edges, etc : 34, 306, 18
Order of s0s1s2 : 306
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) :
3-fold quotients : {34,6}*408
9-fold quotients : {34,2}*136
17-fold quotients : {2,18}*72
18-fold quotients : {17,2}*68
34-fold quotients : {2,9}*36
51-fold quotients : {2,6}*24
102-fold quotients : {2,3}*12
153-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 4, 49)( 5, 50)( 6, 51)( 7, 46)( 8, 47)( 9, 48)( 10, 43)( 11, 44)
( 12, 45)( 13, 40)( 14, 41)( 15, 42)( 16, 37)( 17, 38)( 18, 39)( 19, 34)
( 20, 35)( 21, 36)( 22, 31)( 23, 32)( 24, 33)( 25, 28)( 26, 29)( 27, 30)
( 55,100)( 56,101)( 57,102)( 58, 97)( 59, 98)( 60, 99)( 61, 94)( 62, 95)
( 63, 96)( 64, 91)( 65, 92)( 66, 93)( 67, 88)( 68, 89)( 69, 90)( 70, 85)
( 71, 86)( 72, 87)( 73, 82)( 74, 83)( 75, 84)( 76, 79)( 77, 80)( 78, 81)
(106,151)(107,152)(108,153)(109,148)(110,149)(111,150)(112,145)(113,146)
(114,147)(115,142)(116,143)(117,144)(118,139)(119,140)(120,141)(121,136)
(122,137)(123,138)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)
(157,202)(158,203)(159,204)(160,199)(161,200)(162,201)(163,196)(164,197)
(165,198)(166,193)(167,194)(168,195)(169,190)(170,191)(171,192)(172,187)
(173,188)(174,189)(175,184)(176,185)(177,186)(178,181)(179,182)(180,183)
(208,253)(209,254)(210,255)(211,250)(212,251)(213,252)(214,247)(215,248)
(216,249)(217,244)(218,245)(219,246)(220,241)(221,242)(222,243)(223,238)
(224,239)(225,240)(226,235)(227,236)(228,237)(229,232)(230,233)(231,234)
(259,304)(260,305)(261,306)(262,301)(263,302)(264,303)(265,298)(266,299)
(267,300)(268,295)(269,296)(270,297)(271,292)(272,293)(273,294)(274,289)
(275,290)(276,291)(277,286)(278,287)(279,288)(280,283)(281,284)(282,285);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 49)( 8, 51)( 9, 50)( 10, 46)( 11, 48)
( 12, 47)( 13, 43)( 14, 45)( 15, 44)( 16, 40)( 17, 42)( 18, 41)( 19, 37)
( 20, 39)( 21, 38)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)( 27, 32)
( 29, 30)( 52,107)( 53,106)( 54,108)( 55,104)( 56,103)( 57,105)( 58,152)
( 59,151)( 60,153)( 61,149)( 62,148)( 63,150)( 64,146)( 65,145)( 66,147)
( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)( 73,137)( 74,136)
( 75,138)( 76,134)( 77,133)( 78,135)( 79,131)( 80,130)( 81,132)( 82,128)
( 83,127)( 84,129)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)
( 91,119)( 92,118)( 93,120)( 94,116)( 95,115)( 96,117)( 97,113)( 98,112)
( 99,114)(100,110)(101,109)(102,111)(154,157)(155,159)(156,158)(160,202)
(161,204)(162,203)(163,199)(164,201)(165,200)(166,196)(167,198)(168,197)
(169,193)(170,195)(171,194)(172,190)(173,192)(174,191)(175,187)(176,189)
(177,188)(178,184)(179,186)(180,185)(182,183)(205,260)(206,259)(207,261)
(208,257)(209,256)(210,258)(211,305)(212,304)(213,306)(214,302)(215,301)
(216,303)(217,299)(218,298)(219,300)(220,296)(221,295)(222,297)(223,293)
(224,292)(225,294)(226,290)(227,289)(228,291)(229,287)(230,286)(231,288)
(232,284)(233,283)(234,285)(235,281)(236,280)(237,282)(238,278)(239,277)
(240,279)(241,275)(242,274)(243,276)(244,272)(245,271)(246,273)(247,269)
(248,268)(249,270)(250,266)(251,265)(252,267)(253,263)(254,262)(255,264);;
s2 := ( 1,205)( 2,207)( 3,206)( 4,208)( 5,210)( 6,209)( 7,211)( 8,213)
( 9,212)( 10,214)( 11,216)( 12,215)( 13,217)( 14,219)( 15,218)( 16,220)
( 17,222)( 18,221)( 19,223)( 20,225)( 21,224)( 22,226)( 23,228)( 24,227)
( 25,229)( 26,231)( 27,230)( 28,232)( 29,234)( 30,233)( 31,235)( 32,237)
( 33,236)( 34,238)( 35,240)( 36,239)( 37,241)( 38,243)( 39,242)( 40,244)
( 41,246)( 42,245)( 43,247)( 44,249)( 45,248)( 46,250)( 47,252)( 48,251)
( 49,253)( 50,255)( 51,254)( 52,154)( 53,156)( 54,155)( 55,157)( 56,159)
( 57,158)( 58,160)( 59,162)( 60,161)( 61,163)( 62,165)( 63,164)( 64,166)
( 65,168)( 66,167)( 67,169)( 68,171)( 69,170)( 70,172)( 71,174)( 72,173)
( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,181)( 80,183)
( 81,182)( 82,184)( 83,186)( 84,185)( 85,187)( 86,189)( 87,188)( 88,190)
( 89,192)( 90,191)( 91,193)( 92,195)( 93,194)( 94,196)( 95,198)( 96,197)
( 97,199)( 98,201)( 99,200)(100,202)(101,204)(102,203)(103,257)(104,256)
(105,258)(106,260)(107,259)(108,261)(109,263)(110,262)(111,264)(112,266)
(113,265)(114,267)(115,269)(116,268)(117,270)(118,272)(119,271)(120,273)
(121,275)(122,274)(123,276)(124,278)(125,277)(126,279)(127,281)(128,280)
(129,282)(130,284)(131,283)(132,285)(133,287)(134,286)(135,288)(136,290)
(137,289)(138,291)(139,293)(140,292)(141,294)(142,296)(143,295)(144,297)
(145,299)(146,298)(147,300)(148,302)(149,301)(150,303)(151,305)(152,304)
(153,306);;
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,
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(306)!( 4, 49)( 5, 50)( 6, 51)( 7, 46)( 8, 47)( 9, 48)( 10, 43)
( 11, 44)( 12, 45)( 13, 40)( 14, 41)( 15, 42)( 16, 37)( 17, 38)( 18, 39)
( 19, 34)( 20, 35)( 21, 36)( 22, 31)( 23, 32)( 24, 33)( 25, 28)( 26, 29)
( 27, 30)( 55,100)( 56,101)( 57,102)( 58, 97)( 59, 98)( 60, 99)( 61, 94)
( 62, 95)( 63, 96)( 64, 91)( 65, 92)( 66, 93)( 67, 88)( 68, 89)( 69, 90)
( 70, 85)( 71, 86)( 72, 87)( 73, 82)( 74, 83)( 75, 84)( 76, 79)( 77, 80)
( 78, 81)(106,151)(107,152)(108,153)(109,148)(110,149)(111,150)(112,145)
(113,146)(114,147)(115,142)(116,143)(117,144)(118,139)(119,140)(120,141)
(121,136)(122,137)(123,138)(124,133)(125,134)(126,135)(127,130)(128,131)
(129,132)(157,202)(158,203)(159,204)(160,199)(161,200)(162,201)(163,196)
(164,197)(165,198)(166,193)(167,194)(168,195)(169,190)(170,191)(171,192)
(172,187)(173,188)(174,189)(175,184)(176,185)(177,186)(178,181)(179,182)
(180,183)(208,253)(209,254)(210,255)(211,250)(212,251)(213,252)(214,247)
(215,248)(216,249)(217,244)(218,245)(219,246)(220,241)(221,242)(222,243)
(223,238)(224,239)(225,240)(226,235)(227,236)(228,237)(229,232)(230,233)
(231,234)(259,304)(260,305)(261,306)(262,301)(263,302)(264,303)(265,298)
(266,299)(267,300)(268,295)(269,296)(270,297)(271,292)(272,293)(273,294)
(274,289)(275,290)(276,291)(277,286)(278,287)(279,288)(280,283)(281,284)
(282,285);
s1 := Sym(306)!( 1, 4)( 2, 6)( 3, 5)( 7, 49)( 8, 51)( 9, 50)( 10, 46)
( 11, 48)( 12, 47)( 13, 43)( 14, 45)( 15, 44)( 16, 40)( 17, 42)( 18, 41)
( 19, 37)( 20, 39)( 21, 38)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)
( 27, 32)( 29, 30)( 52,107)( 53,106)( 54,108)( 55,104)( 56,103)( 57,105)
( 58,152)( 59,151)( 60,153)( 61,149)( 62,148)( 63,150)( 64,146)( 65,145)
( 66,147)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)( 73,137)
( 74,136)( 75,138)( 76,134)( 77,133)( 78,135)( 79,131)( 80,130)( 81,132)
( 82,128)( 83,127)( 84,129)( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)
( 90,123)( 91,119)( 92,118)( 93,120)( 94,116)( 95,115)( 96,117)( 97,113)
( 98,112)( 99,114)(100,110)(101,109)(102,111)(154,157)(155,159)(156,158)
(160,202)(161,204)(162,203)(163,199)(164,201)(165,200)(166,196)(167,198)
(168,197)(169,193)(170,195)(171,194)(172,190)(173,192)(174,191)(175,187)
(176,189)(177,188)(178,184)(179,186)(180,185)(182,183)(205,260)(206,259)
(207,261)(208,257)(209,256)(210,258)(211,305)(212,304)(213,306)(214,302)
(215,301)(216,303)(217,299)(218,298)(219,300)(220,296)(221,295)(222,297)
(223,293)(224,292)(225,294)(226,290)(227,289)(228,291)(229,287)(230,286)
(231,288)(232,284)(233,283)(234,285)(235,281)(236,280)(237,282)(238,278)
(239,277)(240,279)(241,275)(242,274)(243,276)(244,272)(245,271)(246,273)
(247,269)(248,268)(249,270)(250,266)(251,265)(252,267)(253,263)(254,262)
(255,264);
s2 := Sym(306)!( 1,205)( 2,207)( 3,206)( 4,208)( 5,210)( 6,209)( 7,211)
( 8,213)( 9,212)( 10,214)( 11,216)( 12,215)( 13,217)( 14,219)( 15,218)
( 16,220)( 17,222)( 18,221)( 19,223)( 20,225)( 21,224)( 22,226)( 23,228)
( 24,227)( 25,229)( 26,231)( 27,230)( 28,232)( 29,234)( 30,233)( 31,235)
( 32,237)( 33,236)( 34,238)( 35,240)( 36,239)( 37,241)( 38,243)( 39,242)
( 40,244)( 41,246)( 42,245)( 43,247)( 44,249)( 45,248)( 46,250)( 47,252)
( 48,251)( 49,253)( 50,255)( 51,254)( 52,154)( 53,156)( 54,155)( 55,157)
( 56,159)( 57,158)( 58,160)( 59,162)( 60,161)( 61,163)( 62,165)( 63,164)
( 64,166)( 65,168)( 66,167)( 67,169)( 68,171)( 69,170)( 70,172)( 71,174)
( 72,173)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,181)
( 80,183)( 81,182)( 82,184)( 83,186)( 84,185)( 85,187)( 86,189)( 87,188)
( 88,190)( 89,192)( 90,191)( 91,193)( 92,195)( 93,194)( 94,196)( 95,198)
( 96,197)( 97,199)( 98,201)( 99,200)(100,202)(101,204)(102,203)(103,257)
(104,256)(105,258)(106,260)(107,259)(108,261)(109,263)(110,262)(111,264)
(112,266)(113,265)(114,267)(115,269)(116,268)(117,270)(118,272)(119,271)
(120,273)(121,275)(122,274)(123,276)(124,278)(125,277)(126,279)(127,281)
(128,280)(129,282)(130,284)(131,283)(132,285)(133,287)(134,286)(135,288)
(136,290)(137,289)(138,291)(139,293)(140,292)(141,294)(142,296)(143,295)
(144,297)(145,299)(146,298)(147,300)(148,302)(149,301)(150,303)(151,305)
(152,304)(153,306);
poly := sub<Sym(306)|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,
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