Polytope of Type {46,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,14}*1288
Also Known As : {46,14|2}. if this polytope has another name.
Group : SmallGroup(1288,31)
Rank : 3
Schlafli Type : {46,14}
Number of vertices, edges, etc : 46, 322, 14
Order of s0s1s2 : 322
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) :
7-fold quotients : {46,2}*184
14-fold quotients : {23,2}*92
23-fold quotients : {2,14}*56
46-fold quotients : {2,7}*28
161-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)
( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)
( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)
( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)( 97,112)
( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(117,138)
(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)
(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)
(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)(165,182)
(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174)
(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)
(194,199)(195,198)(196,197)(209,230)(210,229)(211,228)(212,227)(213,226)
(214,225)(215,224)(216,223)(217,222)(218,221)(219,220)(232,253)(233,252)
(234,251)(235,250)(236,249)(237,248)(238,247)(239,246)(240,245)(241,244)
(242,243)(255,276)(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)
(262,269)(263,268)(264,267)(265,266)(278,299)(279,298)(280,297)(281,296)
(282,295)(283,294)(284,293)(285,292)(286,291)(287,290)(288,289)(301,322)
(302,321)(303,320)(304,319)(305,318)(306,317)(307,316)(308,315)(309,314)
(310,313)(311,312);;
s1 := ( 1, 2)( 3, 23)( 4, 22)( 5, 21)( 6, 20)( 7, 19)( 8, 18)( 9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24,140)( 25,139)( 26,161)( 27,160)( 28,159)
( 29,158)( 30,157)( 31,156)( 32,155)( 33,154)( 34,153)( 35,152)( 36,151)
( 37,150)( 38,149)( 39,148)( 40,147)( 41,146)( 42,145)( 43,144)( 44,143)
( 45,142)( 46,141)( 47,117)( 48,116)( 49,138)( 50,137)( 51,136)( 52,135)
( 53,134)( 54,133)( 55,132)( 56,131)( 57,130)( 58,129)( 59,128)( 60,127)
( 61,126)( 62,125)( 63,124)( 64,123)( 65,122)( 66,121)( 67,120)( 68,119)
( 69,118)( 70, 94)( 71, 93)( 72,115)( 73,114)( 74,113)( 75,112)( 76,111)
( 77,110)( 78,109)( 79,108)( 80,107)( 81,106)( 82,105)( 83,104)( 84,103)
( 85,102)( 86,101)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 91, 96)( 92, 95)
(162,163)(164,184)(165,183)(166,182)(167,181)(168,180)(169,179)(170,178)
(171,177)(172,176)(173,175)(185,301)(186,300)(187,322)(188,321)(189,320)
(190,319)(191,318)(192,317)(193,316)(194,315)(195,314)(196,313)(197,312)
(198,311)(199,310)(200,309)(201,308)(202,307)(203,306)(204,305)(205,304)
(206,303)(207,302)(208,278)(209,277)(210,299)(211,298)(212,297)(213,296)
(214,295)(215,294)(216,293)(217,292)(218,291)(219,290)(220,289)(221,288)
(222,287)(223,286)(224,285)(225,284)(226,283)(227,282)(228,281)(229,280)
(230,279)(231,255)(232,254)(233,276)(234,275)(235,274)(236,273)(237,272)
(238,271)(239,270)(240,269)(241,268)(242,267)(243,266)(244,265)(245,264)
(246,263)(247,262)(248,261)(249,260)(250,259)(251,258)(252,257)(253,256);;
s2 := ( 1,185)( 2,186)( 3,187)( 4,188)( 5,189)( 6,190)( 7,191)( 8,192)
( 9,193)( 10,194)( 11,195)( 12,196)( 13,197)( 14,198)( 15,199)( 16,200)
( 17,201)( 18,202)( 19,203)( 20,204)( 21,205)( 22,206)( 23,207)( 24,162)
( 25,163)( 26,164)( 27,165)( 28,166)( 29,167)( 30,168)( 31,169)( 32,170)
( 33,171)( 34,172)( 35,173)( 36,174)( 37,175)( 38,176)( 39,177)( 40,178)
( 41,179)( 42,180)( 43,181)( 44,182)( 45,183)( 46,184)( 47,300)( 48,301)
( 49,302)( 50,303)( 51,304)( 52,305)( 53,306)( 54,307)( 55,308)( 56,309)
( 57,310)( 58,311)( 59,312)( 60,313)( 61,314)( 62,315)( 63,316)( 64,317)
( 65,318)( 66,319)( 67,320)( 68,321)( 69,322)( 70,277)( 71,278)( 72,279)
( 73,280)( 74,281)( 75,282)( 76,283)( 77,284)( 78,285)( 79,286)( 80,287)
( 81,288)( 82,289)( 83,290)( 84,291)( 85,292)( 86,293)( 87,294)( 88,295)
( 89,296)( 90,297)( 91,298)( 92,299)( 93,254)( 94,255)( 95,256)( 96,257)
( 97,258)( 98,259)( 99,260)(100,261)(101,262)(102,263)(103,264)(104,265)
(105,266)(106,267)(107,268)(108,269)(109,270)(110,271)(111,272)(112,273)
(113,274)(114,275)(115,276)(116,231)(117,232)(118,233)(119,234)(120,235)
(121,236)(122,237)(123,238)(124,239)(125,240)(126,241)(127,242)(128,243)
(129,244)(130,245)(131,246)(132,247)(133,248)(134,249)(135,250)(136,251)
(137,252)(138,253)(139,208)(140,209)(141,210)(142,211)(143,212)(144,213)
(145,214)(146,215)(147,216)(148,217)(149,218)(150,219)(151,220)(152,221)
(153,222)(154,223)(155,224)(156,225)(157,226)(158,227)(159,228)(160,229)
(161,230);;
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,
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*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(322)!( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)
( 9, 16)( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)
( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)
(125,130)(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)
(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)
(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)
(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)
(193,200)(194,199)(195,198)(196,197)(209,230)(210,229)(211,228)(212,227)
(213,226)(214,225)(215,224)(216,223)(217,222)(218,221)(219,220)(232,253)
(233,252)(234,251)(235,250)(236,249)(237,248)(238,247)(239,246)(240,245)
(241,244)(242,243)(255,276)(256,275)(257,274)(258,273)(259,272)(260,271)
(261,270)(262,269)(263,268)(264,267)(265,266)(278,299)(279,298)(280,297)
(281,296)(282,295)(283,294)(284,293)(285,292)(286,291)(287,290)(288,289)
(301,322)(302,321)(303,320)(304,319)(305,318)(306,317)(307,316)(308,315)
(309,314)(310,313)(311,312);
s1 := Sym(322)!( 1, 2)( 3, 23)( 4, 22)( 5, 21)( 6, 20)( 7, 19)( 8, 18)
( 9, 17)( 10, 16)( 11, 15)( 12, 14)( 24,140)( 25,139)( 26,161)( 27,160)
( 28,159)( 29,158)( 30,157)( 31,156)( 32,155)( 33,154)( 34,153)( 35,152)
( 36,151)( 37,150)( 38,149)( 39,148)( 40,147)( 41,146)( 42,145)( 43,144)
( 44,143)( 45,142)( 46,141)( 47,117)( 48,116)( 49,138)( 50,137)( 51,136)
( 52,135)( 53,134)( 54,133)( 55,132)( 56,131)( 57,130)( 58,129)( 59,128)
( 60,127)( 61,126)( 62,125)( 63,124)( 64,123)( 65,122)( 66,121)( 67,120)
( 68,119)( 69,118)( 70, 94)( 71, 93)( 72,115)( 73,114)( 74,113)( 75,112)
( 76,111)( 77,110)( 78,109)( 79,108)( 80,107)( 81,106)( 82,105)( 83,104)
( 84,103)( 85,102)( 86,101)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 91, 96)
( 92, 95)(162,163)(164,184)(165,183)(166,182)(167,181)(168,180)(169,179)
(170,178)(171,177)(172,176)(173,175)(185,301)(186,300)(187,322)(188,321)
(189,320)(190,319)(191,318)(192,317)(193,316)(194,315)(195,314)(196,313)
(197,312)(198,311)(199,310)(200,309)(201,308)(202,307)(203,306)(204,305)
(205,304)(206,303)(207,302)(208,278)(209,277)(210,299)(211,298)(212,297)
(213,296)(214,295)(215,294)(216,293)(217,292)(218,291)(219,290)(220,289)
(221,288)(222,287)(223,286)(224,285)(225,284)(226,283)(227,282)(228,281)
(229,280)(230,279)(231,255)(232,254)(233,276)(234,275)(235,274)(236,273)
(237,272)(238,271)(239,270)(240,269)(241,268)(242,267)(243,266)(244,265)
(245,264)(246,263)(247,262)(248,261)(249,260)(250,259)(251,258)(252,257)
(253,256);
s2 := Sym(322)!( 1,185)( 2,186)( 3,187)( 4,188)( 5,189)( 6,190)( 7,191)
( 8,192)( 9,193)( 10,194)( 11,195)( 12,196)( 13,197)( 14,198)( 15,199)
( 16,200)( 17,201)( 18,202)( 19,203)( 20,204)( 21,205)( 22,206)( 23,207)
( 24,162)( 25,163)( 26,164)( 27,165)( 28,166)( 29,167)( 30,168)( 31,169)
( 32,170)( 33,171)( 34,172)( 35,173)( 36,174)( 37,175)( 38,176)( 39,177)
( 40,178)( 41,179)( 42,180)( 43,181)( 44,182)( 45,183)( 46,184)( 47,300)
( 48,301)( 49,302)( 50,303)( 51,304)( 52,305)( 53,306)( 54,307)( 55,308)
( 56,309)( 57,310)( 58,311)( 59,312)( 60,313)( 61,314)( 62,315)( 63,316)
( 64,317)( 65,318)( 66,319)( 67,320)( 68,321)( 69,322)( 70,277)( 71,278)
( 72,279)( 73,280)( 74,281)( 75,282)( 76,283)( 77,284)( 78,285)( 79,286)
( 80,287)( 81,288)( 82,289)( 83,290)( 84,291)( 85,292)( 86,293)( 87,294)
( 88,295)( 89,296)( 90,297)( 91,298)( 92,299)( 93,254)( 94,255)( 95,256)
( 96,257)( 97,258)( 98,259)( 99,260)(100,261)(101,262)(102,263)(103,264)
(104,265)(105,266)(106,267)(107,268)(108,269)(109,270)(110,271)(111,272)
(112,273)(113,274)(114,275)(115,276)(116,231)(117,232)(118,233)(119,234)
(120,235)(121,236)(122,237)(123,238)(124,239)(125,240)(126,241)(127,242)
(128,243)(129,244)(130,245)(131,246)(132,247)(133,248)(134,249)(135,250)
(136,251)(137,252)(138,253)(139,208)(140,209)(141,210)(142,211)(143,212)
(144,213)(145,214)(146,215)(147,216)(148,217)(149,218)(150,219)(151,220)
(152,221)(153,222)(154,223)(155,224)(156,225)(157,226)(158,227)(159,228)
(160,229)(161,230);
poly := sub<Sym(322)|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,
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*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