Polytope of Type {55,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {55,10}*1100
if this polytope has a name.
Group : SmallGroup(1100,44)
Rank : 3
Schlafli Type : {55,10}
Number of vertices, edges, etc : 55, 275, 10
Order of s₀s₁s₂ : 110
Order of s₀s₁s₂s₁ : 10
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) :
   5-fold quotients : {55,2}*220
   11-fold quotients : {5,10}*100
   25-fold quotients : {11,2}*44
   55-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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