Polytope of Type {10,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,44}*880
Also Known As : {10,44|2}. if this polytope has another name.
Group : SmallGroup(880,161)
Rank : 3
Schlafli Type : {10,44}
Number of vertices, edges, etc : 10, 220, 44
Order of s₀s₁s₂ : 220
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,44,2} of size 1760
Vertex Figure Of :
   {2,10,44} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,22}*440
   5-fold quotients : {2,44}*176
   10-fold quotients : {2,22}*88
   11-fold quotients : {10,4}*80
   20-fold quotients : {2,11}*44
   22-fold quotients : {10,2}*40
   44-fold quotients : {5,2}*20
   55-fold quotients : {2,4}*16
   110-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,88}*1760, {20,44}*1760
Permutation Representation (GAP) :

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