Polytope of Type {40,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,14}*1120
Also Known As : {40,14|2}. if this polytope has another name.
Group : SmallGroup(1120,302)
Rank : 3
Schlafli Type : {40,14}
Number of vertices, edges, etc : 40, 280, 14
Order of s₀s₁s₂ : 280
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 : {20,14}*560
   4-fold quotients : {10,14}*280
   5-fold quotients : {8,14}*224
   7-fold quotients : {40,2}*160
   10-fold quotients : {4,14}*112
   14-fold quotients : {20,2}*80
   20-fold quotients : {2,14}*56
   28-fold quotients : {10,2}*40
   35-fold quotients : {8,2}*32
   40-fold quotients : {2,7}*28
   56-fold quotients : {5,2}*20
   70-fold quotients : {4,2}*16
   140-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 22)
( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 64)( 44, 65)
( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 57)( 51, 58)( 52, 59)
( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 71,106)( 72,107)( 73,108)( 74,109)
( 75,110)( 76,111)( 77,112)( 78,134)( 79,135)( 80,136)( 81,137)( 82,138)
( 83,139)( 84,140)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)( 90,132)
( 91,133)( 92,120)( 93,121)( 94,122)( 95,123)( 96,124)( 97,125)( 98,126)
( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119)(141,211)
(142,212)(143,213)(144,214)(145,215)(146,216)(147,217)(148,239)(149,240)
(150,241)(151,242)(152,243)(153,244)(154,245)(155,232)(156,233)(157,234)
(158,235)(159,236)(160,237)(161,238)(162,225)(163,226)(164,227)(165,228)
(166,229)(167,230)(168,231)(169,218)(170,219)(171,220)(172,221)(173,222)
(174,223)(175,224)(176,246)(177,247)(178,248)(179,249)(180,250)(181,251)
(182,252)(183,274)(184,275)(185,276)(186,277)(187,278)(188,279)(189,280)
(190,267)(191,268)(192,269)(193,270)(194,271)(195,272)(196,273)(197,260)
(198,261)(199,262)(200,263)(201,264)(202,265)(203,266)(204,253)(205,254)
(206,255)(207,256)(208,257)(209,258)(210,259);;
s1 := (  1,148)(  2,154)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)(  8,141)
(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,169)( 16,175)
( 17,174)( 18,173)( 19,172)( 20,171)( 21,170)( 22,162)( 23,168)( 24,167)
( 25,166)( 26,165)( 27,164)( 28,163)( 29,155)( 30,161)( 31,160)( 32,159)
( 33,158)( 34,157)( 35,156)( 36,183)( 37,189)( 38,188)( 39,187)( 40,186)
( 41,185)( 42,184)( 43,176)( 44,182)( 45,181)( 46,180)( 47,179)( 48,178)
( 49,177)( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)( 56,205)
( 57,197)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)( 64,190)
( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,253)( 72,259)
( 73,258)( 74,257)( 75,256)( 76,255)( 77,254)( 78,246)( 79,252)( 80,251)
( 81,250)( 82,249)( 83,248)( 84,247)( 85,274)( 86,280)( 87,279)( 88,278)
( 89,277)( 90,276)( 91,275)( 92,267)( 93,273)( 94,272)( 95,271)( 96,270)
( 97,269)( 98,268)( 99,260)(100,266)(101,265)(102,264)(103,263)(104,262)
(105,261)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)
(113,211)(114,217)(115,216)(116,215)(117,214)(118,213)(119,212)(120,239)
(121,245)(122,244)(123,243)(124,242)(125,241)(126,240)(127,232)(128,238)
(129,237)(130,236)(131,235)(132,234)(133,233)(134,225)(135,231)(136,230)
(137,229)(138,228)(139,227)(140,226);;
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);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(280)!(  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)
( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 64)
( 44, 65)( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 57)( 51, 58)
( 52, 59)( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 71,106)( 72,107)( 73,108)
( 74,109)( 75,110)( 76,111)( 77,112)( 78,134)( 79,135)( 80,136)( 81,137)
( 82,138)( 83,139)( 84,140)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)
( 90,132)( 91,133)( 92,120)( 93,121)( 94,122)( 95,123)( 96,124)( 97,125)
( 98,126)( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119)
(141,211)(142,212)(143,213)(144,214)(145,215)(146,216)(147,217)(148,239)
(149,240)(150,241)(151,242)(152,243)(153,244)(154,245)(155,232)(156,233)
(157,234)(158,235)(159,236)(160,237)(161,238)(162,225)(163,226)(164,227)
(165,228)(166,229)(167,230)(168,231)(169,218)(170,219)(171,220)(172,221)
(173,222)(174,223)(175,224)(176,246)(177,247)(178,248)(179,249)(180,250)
(181,251)(182,252)(183,274)(184,275)(185,276)(186,277)(187,278)(188,279)
(189,280)(190,267)(191,268)(192,269)(193,270)(194,271)(195,272)(196,273)
(197,260)(198,261)(199,262)(200,263)(201,264)(202,265)(203,266)(204,253)
(205,254)(206,255)(207,256)(208,257)(209,258)(210,259);
s1 := Sym(280)!(  1,148)(  2,154)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)
(  8,141)(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,169)
( 16,175)( 17,174)( 18,173)( 19,172)( 20,171)( 21,170)( 22,162)( 23,168)
( 24,167)( 25,166)( 26,165)( 27,164)( 28,163)( 29,155)( 30,161)( 31,160)
( 32,159)( 33,158)( 34,157)( 35,156)( 36,183)( 37,189)( 38,188)( 39,187)
( 40,186)( 41,185)( 42,184)( 43,176)( 44,182)( 45,181)( 46,180)( 47,179)
( 48,178)( 49,177)( 50,204)( 51,210)( 52,209)( 53,208)( 54,207)( 55,206)
( 56,205)( 57,197)( 58,203)( 59,202)( 60,201)( 61,200)( 62,199)( 63,198)
( 64,190)( 65,196)( 66,195)( 67,194)( 68,193)( 69,192)( 70,191)( 71,253)
( 72,259)( 73,258)( 74,257)( 75,256)( 76,255)( 77,254)( 78,246)( 79,252)
( 80,251)( 81,250)( 82,249)( 83,248)( 84,247)( 85,274)( 86,280)( 87,279)
( 88,278)( 89,277)( 90,276)( 91,275)( 92,267)( 93,273)( 94,272)( 95,271)
( 96,270)( 97,269)( 98,268)( 99,260)(100,266)(101,265)(102,264)(103,263)
(104,262)(105,261)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)
(112,219)(113,211)(114,217)(115,216)(116,215)(117,214)(118,213)(119,212)
(120,239)(121,245)(122,244)(123,243)(124,242)(125,241)(126,240)(127,232)
(128,238)(129,237)(130,236)(131,235)(132,234)(133,233)(134,225)(135,231)
(136,230)(137,229)(138,228)(139,227)(140,226);
s2 := Sym(280)!(  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);
poly := sub<Sym(280)|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 >;

References : None.
to this polytope