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