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Polytope of Type {48,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,14}*1344
Also Known As : {48,14|2}. if this polytope has another name.
Group : SmallGroup(1344,1483)
Rank : 3
Schlafli Type : {48,14}
Number of vertices, edges, etc : 48, 336, 14
Order of s0s1s2 : 336
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 : {24,14}*672
   3-fold quotients : {16,14}*448
   4-fold quotients : {12,14}*336
   6-fold quotients : {8,14}*224
   7-fold quotients : {48,2}*192
   8-fold quotients : {6,14}*168
   12-fold quotients : {4,14}*112
   14-fold quotients : {24,2}*96
   21-fold quotients : {16,2}*64
   24-fold quotients : {2,14}*56
   28-fold quotients : {12,2}*48
   42-fold quotients : {8,2}*32
   48-fold quotients : {2,7}*28
   56-fold quotients : {6,2}*24
   84-fold quotients : {4,2}*16
   112-fold quotients : {3,2}*12
   168-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  8, 15)(  9, 16)( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)( 29, 36)
( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 43, 64)( 44, 65)
( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 78)( 51, 79)( 52, 80)
( 53, 81)( 54, 82)( 55, 83)( 56, 84)( 57, 71)( 58, 72)( 59, 73)( 60, 74)
( 61, 75)( 62, 76)( 63, 77)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)
( 90,132)( 91,133)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)( 97,146)
( 98,147)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)
(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,162)
(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,155)(121,156)
(122,157)(123,158)(124,159)(125,160)(126,161)(169,253)(170,254)(171,255)
(172,256)(173,257)(174,258)(175,259)(176,267)(177,268)(178,269)(179,270)
(180,271)(181,272)(182,273)(183,260)(184,261)(185,262)(186,263)(187,264)
(188,265)(189,266)(190,274)(191,275)(192,276)(193,277)(194,278)(195,279)
(196,280)(197,288)(198,289)(199,290)(200,291)(201,292)(202,293)(203,294)
(204,281)(205,282)(206,283)(207,284)(208,285)(209,286)(210,287)(211,316)
(212,317)(213,318)(214,319)(215,320)(216,321)(217,322)(218,330)(219,331)
(220,332)(221,333)(222,334)(223,335)(224,336)(225,323)(226,324)(227,325)
(228,326)(229,327)(230,328)(231,329)(232,295)(233,296)(234,297)(235,298)
(236,299)(237,300)(238,301)(239,309)(240,310)(241,311)(242,312)(243,313)
(244,314)(245,315)(246,302)(247,303)(248,304)(249,305)(250,306)(251,307)
(252,308);;
s1 := (  1,176)(  2,182)(  3,181)(  4,180)(  5,179)(  6,178)(  7,177)(  8,169)
(  9,175)( 10,174)( 11,173)( 12,172)( 13,171)( 14,170)( 15,183)( 16,189)
( 17,188)( 18,187)( 19,186)( 20,185)( 21,184)( 22,197)( 23,203)( 24,202)
( 25,201)( 26,200)( 27,199)( 28,198)( 29,190)( 30,196)( 31,195)( 32,194)
( 33,193)( 34,192)( 35,191)( 36,204)( 37,210)( 38,209)( 39,208)( 40,207)
( 41,206)( 42,205)( 43,239)( 44,245)( 45,244)( 46,243)( 47,242)( 48,241)
( 49,240)( 50,232)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,233)
( 57,246)( 58,252)( 59,251)( 60,250)( 61,249)( 62,248)( 63,247)( 64,218)
( 65,224)( 66,223)( 67,222)( 68,221)( 69,220)( 70,219)( 71,211)( 72,217)
( 73,216)( 74,215)( 75,214)( 76,213)( 77,212)( 78,225)( 79,231)( 80,230)
( 81,229)( 82,228)( 83,227)( 84,226)( 85,302)( 86,308)( 87,307)( 88,306)
( 89,305)( 90,304)( 91,303)( 92,295)( 93,301)( 94,300)( 95,299)( 96,298)
( 97,297)( 98,296)( 99,309)(100,315)(101,314)(102,313)(103,312)(104,311)
(105,310)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)
(113,316)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)(120,330)
(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,260)(128,266)
(129,265)(130,264)(131,263)(132,262)(133,261)(134,253)(135,259)(136,258)
(137,257)(138,256)(139,255)(140,254)(141,267)(142,273)(143,272)(144,271)
(145,270)(146,269)(147,268)(148,281)(149,287)(150,286)(151,285)(152,284)
(153,283)(154,282)(155,274)(156,280)(157,279)(158,278)(159,277)(160,276)
(161,275)(162,288)(163,294)(164,293)(165,292)(166,291)(167,290)(168,289);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)
( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)
( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)
(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)
(130,132)(134,135)(136,140)(137,139)(141,142)(143,147)(144,146)(148,149)
(150,154)(151,153)(155,156)(157,161)(158,160)(162,163)(164,168)(165,167)
(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)(183,184)(185,189)
(186,188)(190,191)(192,196)(193,195)(197,198)(199,203)(200,202)(204,205)
(206,210)(207,209)(211,212)(213,217)(214,216)(218,219)(220,224)(221,223)
(225,226)(227,231)(228,230)(232,233)(234,238)(235,237)(239,240)(241,245)
(242,244)(246,247)(248,252)(249,251)(253,254)(255,259)(256,258)(260,261)
(262,266)(263,265)(267,268)(269,273)(270,272)(274,275)(276,280)(277,279)
(281,282)(283,287)(284,286)(288,289)(290,294)(291,293)(295,296)(297,301)
(298,300)(302,303)(304,308)(305,307)(309,310)(311,315)(312,314)(316,317)
(318,322)(319,321)(323,324)(325,329)(326,328)(330,331)(332,336)(333,335);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(336)!(  8, 15)(  9, 16)( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)
( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 43, 64)
( 44, 65)( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 78)( 51, 79)
( 52, 80)( 53, 81)( 54, 82)( 55, 83)( 56, 84)( 57, 71)( 58, 72)( 59, 73)
( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 85,127)( 86,128)( 87,129)( 88,130)
( 89,131)( 90,132)( 91,133)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)
( 97,146)( 98,147)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)
(105,140)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)
(113,162)(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,155)
(121,156)(122,157)(123,158)(124,159)(125,160)(126,161)(169,253)(170,254)
(171,255)(172,256)(173,257)(174,258)(175,259)(176,267)(177,268)(178,269)
(179,270)(180,271)(181,272)(182,273)(183,260)(184,261)(185,262)(186,263)
(187,264)(188,265)(189,266)(190,274)(191,275)(192,276)(193,277)(194,278)
(195,279)(196,280)(197,288)(198,289)(199,290)(200,291)(201,292)(202,293)
(203,294)(204,281)(205,282)(206,283)(207,284)(208,285)(209,286)(210,287)
(211,316)(212,317)(213,318)(214,319)(215,320)(216,321)(217,322)(218,330)
(219,331)(220,332)(221,333)(222,334)(223,335)(224,336)(225,323)(226,324)
(227,325)(228,326)(229,327)(230,328)(231,329)(232,295)(233,296)(234,297)
(235,298)(236,299)(237,300)(238,301)(239,309)(240,310)(241,311)(242,312)
(243,313)(244,314)(245,315)(246,302)(247,303)(248,304)(249,305)(250,306)
(251,307)(252,308);
s1 := Sym(336)!(  1,176)(  2,182)(  3,181)(  4,180)(  5,179)(  6,178)(  7,177)
(  8,169)(  9,175)( 10,174)( 11,173)( 12,172)( 13,171)( 14,170)( 15,183)
( 16,189)( 17,188)( 18,187)( 19,186)( 20,185)( 21,184)( 22,197)( 23,203)
( 24,202)( 25,201)( 26,200)( 27,199)( 28,198)( 29,190)( 30,196)( 31,195)
( 32,194)( 33,193)( 34,192)( 35,191)( 36,204)( 37,210)( 38,209)( 39,208)
( 40,207)( 41,206)( 42,205)( 43,239)( 44,245)( 45,244)( 46,243)( 47,242)
( 48,241)( 49,240)( 50,232)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)
( 56,233)( 57,246)( 58,252)( 59,251)( 60,250)( 61,249)( 62,248)( 63,247)
( 64,218)( 65,224)( 66,223)( 67,222)( 68,221)( 69,220)( 70,219)( 71,211)
( 72,217)( 73,216)( 74,215)( 75,214)( 76,213)( 77,212)( 78,225)( 79,231)
( 80,230)( 81,229)( 82,228)( 83,227)( 84,226)( 85,302)( 86,308)( 87,307)
( 88,306)( 89,305)( 90,304)( 91,303)( 92,295)( 93,301)( 94,300)( 95,299)
( 96,298)( 97,297)( 98,296)( 99,309)(100,315)(101,314)(102,313)(103,312)
(104,311)(105,310)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)
(112,324)(113,316)(114,322)(115,321)(116,320)(117,319)(118,318)(119,317)
(120,330)(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,260)
(128,266)(129,265)(130,264)(131,263)(132,262)(133,261)(134,253)(135,259)
(136,258)(137,257)(138,256)(139,255)(140,254)(141,267)(142,273)(143,272)
(144,271)(145,270)(146,269)(147,268)(148,281)(149,287)(150,286)(151,285)
(152,284)(153,283)(154,282)(155,274)(156,280)(157,279)(158,278)(159,277)
(160,276)(161,275)(162,288)(163,294)(164,293)(165,292)(166,291)(167,290)
(168,289);
s2 := Sym(336)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)
( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)
( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)
(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)
(129,133)(130,132)(134,135)(136,140)(137,139)(141,142)(143,147)(144,146)
(148,149)(150,154)(151,153)(155,156)(157,161)(158,160)(162,163)(164,168)
(165,167)(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)(183,184)
(185,189)(186,188)(190,191)(192,196)(193,195)(197,198)(199,203)(200,202)
(204,205)(206,210)(207,209)(211,212)(213,217)(214,216)(218,219)(220,224)
(221,223)(225,226)(227,231)(228,230)(232,233)(234,238)(235,237)(239,240)
(241,245)(242,244)(246,247)(248,252)(249,251)(253,254)(255,259)(256,258)
(260,261)(262,266)(263,265)(267,268)(269,273)(270,272)(274,275)(276,280)
(277,279)(281,282)(283,287)(284,286)(288,289)(290,294)(291,293)(295,296)
(297,301)(298,300)(302,303)(304,308)(305,307)(309,310)(311,315)(312,314)
(316,317)(318,322)(319,321)(323,324)(325,329)(326,328)(330,331)(332,336)
(333,335);
poly := sub<Sym(336)|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*s0*s1*s0*s1 >; 
 
References : None.
to this polytope