Polytope of Type {18,38}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,38}*1368
Also Known As : {18,38|2}. if this polytope has another name.
Group : SmallGroup(1368,59)
Rank : 3
Schlafli Type : {18,38}
Number of vertices, edges, etc : 18, 342, 38
Order of s0s1s2 : 342
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 : {6,38}*456
9-fold quotients : {2,38}*152
18-fold quotients : {2,19}*76
19-fold quotients : {18,2}*72
38-fold quotients : {9,2}*36
57-fold quotients : {6,2}*24
114-fold quotients : {3,2}*12
171-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)( 53, 54)( 56, 57)( 58,116)( 59,115)( 60,117)( 61,119)( 62,118)
( 63,120)( 64,122)( 65,121)( 66,123)( 67,125)( 68,124)( 69,126)( 70,128)
( 71,127)( 72,129)( 73,131)( 74,130)( 75,132)( 76,134)( 77,133)( 78,135)
( 79,137)( 80,136)( 81,138)( 82,140)( 83,139)( 84,141)( 85,143)( 86,142)
( 87,144)( 88,146)( 89,145)( 90,147)( 91,149)( 92,148)( 93,150)( 94,152)
( 95,151)( 96,153)( 97,155)( 98,154)( 99,156)(100,158)(101,157)(102,159)
(103,161)(104,160)(105,162)(106,164)(107,163)(108,165)(109,167)(110,166)
(111,168)(112,170)(113,169)(114,171)(173,174)(176,177)(179,180)(182,183)
(185,186)(188,189)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)
(209,210)(212,213)(215,216)(218,219)(221,222)(224,225)(227,228)(229,287)
(230,286)(231,288)(232,290)(233,289)(234,291)(235,293)(236,292)(237,294)
(238,296)(239,295)(240,297)(241,299)(242,298)(243,300)(244,302)(245,301)
(246,303)(247,305)(248,304)(249,306)(250,308)(251,307)(252,309)(253,311)
(254,310)(255,312)(256,314)(257,313)(258,315)(259,317)(260,316)(261,318)
(262,320)(263,319)(264,321)(265,323)(266,322)(267,324)(268,326)(269,325)
(270,327)(271,329)(272,328)(273,330)(274,332)(275,331)(276,333)(277,335)
(278,334)(279,336)(280,338)(281,337)(282,339)(283,341)(284,340)(285,342);;
s1 := ( 1, 58)( 2, 60)( 3, 59)( 4,112)( 5,114)( 6,113)( 7,109)( 8,111)
( 9,110)( 10,106)( 11,108)( 12,107)( 13,103)( 14,105)( 15,104)( 16,100)
( 17,102)( 18,101)( 19, 97)( 20, 99)( 21, 98)( 22, 94)( 23, 96)( 24, 95)
( 25, 91)( 26, 93)( 27, 92)( 28, 88)( 29, 90)( 30, 89)( 31, 85)( 32, 87)
( 33, 86)( 34, 82)( 35, 84)( 36, 83)( 37, 79)( 38, 81)( 39, 80)( 40, 76)
( 41, 78)( 42, 77)( 43, 73)( 44, 75)( 45, 74)( 46, 70)( 47, 72)( 48, 71)
( 49, 67)( 50, 69)( 51, 68)( 52, 64)( 53, 66)( 54, 65)( 55, 61)( 56, 63)
( 57, 62)(115,116)(118,170)(119,169)(120,171)(121,167)(122,166)(123,168)
(124,164)(125,163)(126,165)(127,161)(128,160)(129,162)(130,158)(131,157)
(132,159)(133,155)(134,154)(135,156)(136,152)(137,151)(138,153)(139,149)
(140,148)(141,150)(142,146)(143,145)(144,147)(172,229)(173,231)(174,230)
(175,283)(176,285)(177,284)(178,280)(179,282)(180,281)(181,277)(182,279)
(183,278)(184,274)(185,276)(186,275)(187,271)(188,273)(189,272)(190,268)
(191,270)(192,269)(193,265)(194,267)(195,266)(196,262)(197,264)(198,263)
(199,259)(200,261)(201,260)(202,256)(203,258)(204,257)(205,253)(206,255)
(207,254)(208,250)(209,252)(210,251)(211,247)(212,249)(213,248)(214,244)
(215,246)(216,245)(217,241)(218,243)(219,242)(220,238)(221,240)(222,239)
(223,235)(224,237)(225,236)(226,232)(227,234)(228,233)(286,287)(289,341)
(290,340)(291,342)(292,338)(293,337)(294,339)(295,335)(296,334)(297,336)
(298,332)(299,331)(300,333)(301,329)(302,328)(303,330)(304,326)(305,325)
(306,327)(307,323)(308,322)(309,324)(310,320)(311,319)(312,321)(313,317)
(314,316)(315,318);;
s2 := ( 1,175)( 2,176)( 3,177)( 4,172)( 5,173)( 6,174)( 7,226)( 8,227)
( 9,228)( 10,223)( 11,224)( 12,225)( 13,220)( 14,221)( 15,222)( 16,217)
( 17,218)( 18,219)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)( 24,213)
( 25,208)( 26,209)( 27,210)( 28,205)( 29,206)( 30,207)( 31,202)( 32,203)
( 33,204)( 34,199)( 35,200)( 36,201)( 37,196)( 38,197)( 39,198)( 40,193)
( 41,194)( 42,195)( 43,190)( 44,191)( 45,192)( 46,187)( 47,188)( 48,189)
( 49,184)( 50,185)( 51,186)( 52,181)( 53,182)( 54,183)( 55,178)( 56,179)
( 57,180)( 58,232)( 59,233)( 60,234)( 61,229)( 62,230)( 63,231)( 64,283)
( 65,284)( 66,285)( 67,280)( 68,281)( 69,282)( 70,277)( 71,278)( 72,279)
( 73,274)( 74,275)( 75,276)( 76,271)( 77,272)( 78,273)( 79,268)( 80,269)
( 81,270)( 82,265)( 83,266)( 84,267)( 85,262)( 86,263)( 87,264)( 88,259)
( 89,260)( 90,261)( 91,256)( 92,257)( 93,258)( 94,253)( 95,254)( 96,255)
( 97,250)( 98,251)( 99,252)(100,247)(101,248)(102,249)(103,244)(104,245)
(105,246)(106,241)(107,242)(108,243)(109,238)(110,239)(111,240)(112,235)
(113,236)(114,237)(115,289)(116,290)(117,291)(118,286)(119,287)(120,288)
(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,334)(128,335)
(129,336)(130,331)(131,332)(132,333)(133,328)(134,329)(135,330)(136,325)
(137,326)(138,327)(139,322)(140,323)(141,324)(142,319)(143,320)(144,321)
(145,316)(146,317)(147,318)(148,313)(149,314)(150,315)(151,310)(152,311)
(153,312)(154,307)(155,308)(156,309)(157,304)(158,305)(159,306)(160,301)
(161,302)(162,303)(163,298)(164,299)(165,300)(166,295)(167,296)(168,297)
(169,292)(170,293)(171,294);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(342)!( 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)( 53, 54)( 56, 57)( 58,116)( 59,115)( 60,117)( 61,119)
( 62,118)( 63,120)( 64,122)( 65,121)( 66,123)( 67,125)( 68,124)( 69,126)
( 70,128)( 71,127)( 72,129)( 73,131)( 74,130)( 75,132)( 76,134)( 77,133)
( 78,135)( 79,137)( 80,136)( 81,138)( 82,140)( 83,139)( 84,141)( 85,143)
( 86,142)( 87,144)( 88,146)( 89,145)( 90,147)( 91,149)( 92,148)( 93,150)
( 94,152)( 95,151)( 96,153)( 97,155)( 98,154)( 99,156)(100,158)(101,157)
(102,159)(103,161)(104,160)(105,162)(106,164)(107,163)(108,165)(109,167)
(110,166)(111,168)(112,170)(113,169)(114,171)(173,174)(176,177)(179,180)
(182,183)(185,186)(188,189)(191,192)(194,195)(197,198)(200,201)(203,204)
(206,207)(209,210)(212,213)(215,216)(218,219)(221,222)(224,225)(227,228)
(229,287)(230,286)(231,288)(232,290)(233,289)(234,291)(235,293)(236,292)
(237,294)(238,296)(239,295)(240,297)(241,299)(242,298)(243,300)(244,302)
(245,301)(246,303)(247,305)(248,304)(249,306)(250,308)(251,307)(252,309)
(253,311)(254,310)(255,312)(256,314)(257,313)(258,315)(259,317)(260,316)
(261,318)(262,320)(263,319)(264,321)(265,323)(266,322)(267,324)(268,326)
(269,325)(270,327)(271,329)(272,328)(273,330)(274,332)(275,331)(276,333)
(277,335)(278,334)(279,336)(280,338)(281,337)(282,339)(283,341)(284,340)
(285,342);
s1 := Sym(342)!( 1, 58)( 2, 60)( 3, 59)( 4,112)( 5,114)( 6,113)( 7,109)
( 8,111)( 9,110)( 10,106)( 11,108)( 12,107)( 13,103)( 14,105)( 15,104)
( 16,100)( 17,102)( 18,101)( 19, 97)( 20, 99)( 21, 98)( 22, 94)( 23, 96)
( 24, 95)( 25, 91)( 26, 93)( 27, 92)( 28, 88)( 29, 90)( 30, 89)( 31, 85)
( 32, 87)( 33, 86)( 34, 82)( 35, 84)( 36, 83)( 37, 79)( 38, 81)( 39, 80)
( 40, 76)( 41, 78)( 42, 77)( 43, 73)( 44, 75)( 45, 74)( 46, 70)( 47, 72)
( 48, 71)( 49, 67)( 50, 69)( 51, 68)( 52, 64)( 53, 66)( 54, 65)( 55, 61)
( 56, 63)( 57, 62)(115,116)(118,170)(119,169)(120,171)(121,167)(122,166)
(123,168)(124,164)(125,163)(126,165)(127,161)(128,160)(129,162)(130,158)
(131,157)(132,159)(133,155)(134,154)(135,156)(136,152)(137,151)(138,153)
(139,149)(140,148)(141,150)(142,146)(143,145)(144,147)(172,229)(173,231)
(174,230)(175,283)(176,285)(177,284)(178,280)(179,282)(180,281)(181,277)
(182,279)(183,278)(184,274)(185,276)(186,275)(187,271)(188,273)(189,272)
(190,268)(191,270)(192,269)(193,265)(194,267)(195,266)(196,262)(197,264)
(198,263)(199,259)(200,261)(201,260)(202,256)(203,258)(204,257)(205,253)
(206,255)(207,254)(208,250)(209,252)(210,251)(211,247)(212,249)(213,248)
(214,244)(215,246)(216,245)(217,241)(218,243)(219,242)(220,238)(221,240)
(222,239)(223,235)(224,237)(225,236)(226,232)(227,234)(228,233)(286,287)
(289,341)(290,340)(291,342)(292,338)(293,337)(294,339)(295,335)(296,334)
(297,336)(298,332)(299,331)(300,333)(301,329)(302,328)(303,330)(304,326)
(305,325)(306,327)(307,323)(308,322)(309,324)(310,320)(311,319)(312,321)
(313,317)(314,316)(315,318);
s2 := Sym(342)!( 1,175)( 2,176)( 3,177)( 4,172)( 5,173)( 6,174)( 7,226)
( 8,227)( 9,228)( 10,223)( 11,224)( 12,225)( 13,220)( 14,221)( 15,222)
( 16,217)( 17,218)( 18,219)( 19,214)( 20,215)( 21,216)( 22,211)( 23,212)
( 24,213)( 25,208)( 26,209)( 27,210)( 28,205)( 29,206)( 30,207)( 31,202)
( 32,203)( 33,204)( 34,199)( 35,200)( 36,201)( 37,196)( 38,197)( 39,198)
( 40,193)( 41,194)( 42,195)( 43,190)( 44,191)( 45,192)( 46,187)( 47,188)
( 48,189)( 49,184)( 50,185)( 51,186)( 52,181)( 53,182)( 54,183)( 55,178)
( 56,179)( 57,180)( 58,232)( 59,233)( 60,234)( 61,229)( 62,230)( 63,231)
( 64,283)( 65,284)( 66,285)( 67,280)( 68,281)( 69,282)( 70,277)( 71,278)
( 72,279)( 73,274)( 74,275)( 75,276)( 76,271)( 77,272)( 78,273)( 79,268)
( 80,269)( 81,270)( 82,265)( 83,266)( 84,267)( 85,262)( 86,263)( 87,264)
( 88,259)( 89,260)( 90,261)( 91,256)( 92,257)( 93,258)( 94,253)( 95,254)
( 96,255)( 97,250)( 98,251)( 99,252)(100,247)(101,248)(102,249)(103,244)
(104,245)(105,246)(106,241)(107,242)(108,243)(109,238)(110,239)(111,240)
(112,235)(113,236)(114,237)(115,289)(116,290)(117,291)(118,286)(119,287)
(120,288)(121,340)(122,341)(123,342)(124,337)(125,338)(126,339)(127,334)
(128,335)(129,336)(130,331)(131,332)(132,333)(133,328)(134,329)(135,330)
(136,325)(137,326)(138,327)(139,322)(140,323)(141,324)(142,319)(143,320)
(144,321)(145,316)(146,317)(147,318)(148,313)(149,314)(150,315)(151,310)
(152,311)(153,312)(154,307)(155,308)(156,309)(157,304)(158,305)(159,306)
(160,301)(161,302)(162,303)(163,298)(164,299)(165,300)(166,295)(167,296)
(168,297)(169,292)(170,293)(171,294);
poly := sub<Sym(342)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope