Polytope of Type {14,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,40}*1120
Also Known As : {14,40|2}. if this polytope has another name.
Group : SmallGroup(1120,302)
Rank : 3
Schlafli Type : {14,40}
Number of vertices, edges, etc : 14, 280, 40
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 : {14,20}*560
   4-fold quotients : {14,10}*280
   5-fold quotients : {14,8}*224
   7-fold quotients : {2,40}*160
   10-fold quotients : {14,4}*112
   14-fold quotients : {2,20}*80
   20-fold quotients : {14,2}*56
   28-fold quotients : {2,10}*40
   35-fold quotients : {2,8}*32
   40-fold quotients : {7,2}*28
   56-fold quotients : {2,5}*20
   70-fold quotients : {2,4}*16
   140-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);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8, 30)(  9, 29)( 10, 35)( 11, 34)( 12, 33)
( 13, 32)( 14, 31)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)
( 21, 24)( 36, 37)( 38, 42)( 39, 41)( 43, 65)( 44, 64)( 45, 70)( 46, 69)
( 47, 68)( 48, 67)( 49, 66)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)
( 55, 60)( 56, 59)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)
( 77,108)( 78,135)( 79,134)( 80,140)( 81,139)( 82,138)( 83,137)( 84,136)
( 85,128)( 86,127)( 87,133)( 88,132)( 89,131)( 90,130)( 91,129)( 92,121)
( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)( 99,114)(100,113)
(101,119)(102,118)(103,117)(104,116)(105,115)(141,212)(142,211)(143,217)
(144,216)(145,215)(146,214)(147,213)(148,240)(149,239)(150,245)(151,244)
(152,243)(153,242)(154,241)(155,233)(156,232)(157,238)(158,237)(159,236)
(160,235)(161,234)(162,226)(163,225)(164,231)(165,230)(166,229)(167,228)
(168,227)(169,219)(170,218)(171,224)(172,223)(173,222)(174,221)(175,220)
(176,247)(177,246)(178,252)(179,251)(180,250)(181,249)(182,248)(183,275)
(184,274)(185,280)(186,279)(187,278)(188,277)(189,276)(190,268)(191,267)
(192,273)(193,272)(194,271)(195,270)(196,269)(197,261)(198,260)(199,266)
(200,265)(201,264)(202,263)(203,262)(204,254)(205,253)(206,259)(207,258)
(208,257)(209,256)(210,255);;
s2 := (  1,148)(  2,149)(  3,150)(  4,151)(  5,152)(  6,153)(  7,154)(  8,141)
(  9,142)( 10,143)( 11,144)( 12,145)( 13,146)( 14,147)( 15,169)( 16,170)
( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,162)( 23,163)( 24,164)
( 25,165)( 26,166)( 27,167)( 28,168)( 29,155)( 30,156)( 31,157)( 32,158)
( 33,159)( 34,160)( 35,161)( 36,183)( 37,184)( 38,185)( 39,186)( 40,187)
( 41,188)( 42,189)( 43,176)( 44,177)( 45,178)( 46,179)( 47,180)( 48,181)
( 49,182)( 50,204)( 51,205)( 52,206)( 53,207)( 54,208)( 55,209)( 56,210)
( 57,197)( 58,198)( 59,199)( 60,200)( 61,201)( 62,202)( 63,203)( 64,190)
( 65,191)( 66,192)( 67,193)( 68,194)( 69,195)( 70,196)( 71,253)( 72,254)
( 73,255)( 74,256)( 75,257)( 76,258)( 77,259)( 78,246)( 79,247)( 80,248)
( 81,249)( 82,250)( 83,251)( 84,252)( 85,274)( 86,275)( 87,276)( 88,277)
( 89,278)( 90,279)( 91,280)( 92,267)( 93,268)( 94,269)( 95,270)( 96,271)
( 97,272)( 98,273)( 99,260)(100,261)(101,262)(102,263)(103,264)(104,265)
(105,266)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)
(113,211)(114,212)(115,213)(116,214)(117,215)(118,216)(119,217)(120,239)
(121,240)(122,241)(123,242)(124,243)(125,244)(126,245)(127,232)(128,233)
(129,234)(130,235)(131,236)(132,237)(133,238)(134,225)(135,226)(136,227)
(137,228)(138,229)(139,230)(140,231);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope