Polytope of Type {2,10,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,44}*1760
if this polytope has a name.
Group : SmallGroup(1760,1181)
Rank : 4
Schlafli Type : {2,10,44}
Number of vertices, edges, etc : 2, 10, 220, 44
Order of s₀s₁s₂s₃ : 220
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,10,22}*880
   5-fold quotients : {2,2,44}*352
   10-fold quotients : {2,2,22}*176
   11-fold quotients : {2,10,4}*160
   20-fold quotients : {2,2,11}*88
   22-fold quotients : {2,10,2}*80
   44-fold quotients : {2,5,2}*40
   55-fold quotients : {2,2,4}*32
   110-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)( 21, 54)
( 22, 55)( 23, 56)( 24, 57)( 25, 36)( 26, 37)( 27, 38)( 28, 39)( 29, 40)
( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 34, 45)( 35, 46)( 69,102)( 70,103)
( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)( 78,111)
( 79,112)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)
( 87, 98)( 88, 99)( 89,100)( 90,101)(124,157)(125,158)(126,159)(127,160)
(128,161)(129,162)(130,163)(131,164)(132,165)(133,166)(134,167)(135,146)
(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)(143,154)
(144,155)(145,156)(179,212)(180,213)(181,214)(182,215)(183,216)(184,217)
(185,218)(186,219)(187,220)(188,221)(189,222)(190,201)(191,202)(192,203)
(193,204)(194,205)(195,206)(196,207)(197,208)(198,209)(199,210)(200,211);;
s2 := (  3, 14)(  4, 24)(  5, 23)(  6, 22)(  7, 21)(  8, 20)(  9, 19)( 10, 18)
( 11, 17)( 12, 16)( 13, 15)( 25, 47)( 26, 57)( 27, 56)( 28, 55)( 29, 54)
( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)( 37, 46)( 38, 45)
( 39, 44)( 40, 43)( 41, 42)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)
( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 80,102)( 81,112)
( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)( 89,104)
( 90,103)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(113,179)(114,189)
(115,188)(116,187)(117,186)(118,185)(119,184)(120,183)(121,182)(122,181)
(123,180)(124,168)(125,178)(126,177)(127,176)(128,175)(129,174)(130,173)
(131,172)(132,171)(133,170)(134,169)(135,212)(136,222)(137,221)(138,220)
(139,219)(140,218)(141,217)(142,216)(143,215)(144,214)(145,213)(146,201)
(147,211)(148,210)(149,209)(150,208)(151,207)(152,206)(153,205)(154,204)
(155,203)(156,202)(157,190)(158,200)(159,199)(160,198)(161,197)(162,196)
(163,195)(164,194)(165,193)(166,192)(167,191);;
s3 := (  3,114)(  4,113)(  5,123)(  6,122)(  7,121)(  8,120)(  9,119)( 10,118)
( 11,117)( 12,116)( 13,115)( 14,125)( 15,124)( 16,134)( 17,133)( 18,132)
( 19,131)( 20,130)( 21,129)( 22,128)( 23,127)( 24,126)( 25,136)( 26,135)
( 27,145)( 28,144)( 29,143)( 30,142)( 31,141)( 32,140)( 33,139)( 34,138)
( 35,137)( 36,147)( 37,146)( 38,156)( 39,155)( 40,154)( 41,153)( 42,152)
( 43,151)( 44,150)( 45,149)( 46,148)( 47,158)( 48,157)( 49,167)( 50,166)
( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)( 58,169)
( 59,168)( 60,178)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)( 66,172)
( 67,171)( 68,170)( 69,180)( 70,179)( 71,189)( 72,188)( 73,187)( 74,186)
( 75,185)( 76,184)( 77,183)( 78,182)( 79,181)( 80,191)( 81,190)( 82,200)
( 83,199)( 84,198)( 85,197)( 86,196)( 87,195)( 88,194)( 89,193)( 90,192)
( 91,202)( 92,201)( 93,211)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)
( 99,205)(100,204)(101,203)(102,213)(103,212)(104,222)(105,221)(106,220)
(107,219)(108,218)(109,217)(110,216)(111,215)(112,214);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(222)!(1,2);
s1 := Sym(222)!( 14, 47)( 15, 48)( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)
( 21, 54)( 22, 55)( 23, 56)( 24, 57)( 25, 36)( 26, 37)( 27, 38)( 28, 39)
( 29, 40)( 30, 41)( 31, 42)( 32, 43)( 33, 44)( 34, 45)( 35, 46)( 69,102)
( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)
( 78,111)( 79,112)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)
( 86, 97)( 87, 98)( 88, 99)( 89,100)( 90,101)(124,157)(125,158)(126,159)
(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)(133,166)(134,167)
(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)
(143,154)(144,155)(145,156)(179,212)(180,213)(181,214)(182,215)(183,216)
(184,217)(185,218)(186,219)(187,220)(188,221)(189,222)(190,201)(191,202)
(192,203)(193,204)(194,205)(195,206)(196,207)(197,208)(198,209)(199,210)
(200,211);
s2 := Sym(222)!(  3, 14)(  4, 24)(  5, 23)(  6, 22)(  7, 21)(  8, 20)(  9, 19)
( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 25, 47)( 26, 57)( 27, 56)( 28, 55)
( 29, 54)( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 58, 69)( 59, 79)( 60, 78)( 61, 77)
( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 80,102)
( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)
( 89,104)( 90,103)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(113,179)
(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,183)(121,182)
(122,181)(123,180)(124,168)(125,178)(126,177)(127,176)(128,175)(129,174)
(130,173)(131,172)(132,171)(133,170)(134,169)(135,212)(136,222)(137,221)
(138,220)(139,219)(140,218)(141,217)(142,216)(143,215)(144,214)(145,213)
(146,201)(147,211)(148,210)(149,209)(150,208)(151,207)(152,206)(153,205)
(154,204)(155,203)(156,202)(157,190)(158,200)(159,199)(160,198)(161,197)
(162,196)(163,195)(164,194)(165,193)(166,192)(167,191);
s3 := Sym(222)!(  3,114)(  4,113)(  5,123)(  6,122)(  7,121)(  8,120)(  9,119)
( 10,118)( 11,117)( 12,116)( 13,115)( 14,125)( 15,124)( 16,134)( 17,133)
( 18,132)( 19,131)( 20,130)( 21,129)( 22,128)( 23,127)( 24,126)( 25,136)
( 26,135)( 27,145)( 28,144)( 29,143)( 30,142)( 31,141)( 32,140)( 33,139)
( 34,138)( 35,137)( 36,147)( 37,146)( 38,156)( 39,155)( 40,154)( 41,153)
( 42,152)( 43,151)( 44,150)( 45,149)( 46,148)( 47,158)( 48,157)( 49,167)
( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)
( 58,169)( 59,168)( 60,178)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)
( 66,172)( 67,171)( 68,170)( 69,180)( 70,179)( 71,189)( 72,188)( 73,187)
( 74,186)( 75,185)( 76,184)( 77,183)( 78,182)( 79,181)( 80,191)( 81,190)
( 82,200)( 83,199)( 84,198)( 85,197)( 86,196)( 87,195)( 88,194)( 89,193)
( 90,192)( 91,202)( 92,201)( 93,211)( 94,210)( 95,209)( 96,208)( 97,207)
( 98,206)( 99,205)(100,204)(101,203)(102,213)(103,212)(104,222)(105,221)
(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214);
poly := sub<Sym(222)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope