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