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Polytope of Type {2,44,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,44,10}*1760
if this polytope has a name.
Group : SmallGroup(1760,1181)
Rank : 4
Schlafli Type : {2,44,10}
Number of vertices, edges, etc : 2, 44, 220, 10
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 : {2,22,10}*880
   5-fold quotients : {2,44,2}*352
   10-fold quotients : {2,22,2}*176
   11-fold quotients : {2,4,10}*160
   20-fold quotients : {2,11,2}*88
   22-fold quotients : {2,2,10}*80
   44-fold quotients : {2,2,5}*40
   55-fold quotients : {2,4,2}*32
   110-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)
( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)( 71, 78)
( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)
( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)(105,110)
(106,109)(107,108)(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)
(119,173)(120,172)(121,171)(122,170)(123,169)(124,179)(125,189)(126,188)
(127,187)(128,186)(129,185)(130,184)(131,183)(132,182)(133,181)(134,180)
(135,190)(136,200)(137,199)(138,198)(139,197)(140,196)(141,195)(142,194)
(143,193)(144,192)(145,191)(146,201)(147,211)(148,210)(149,209)(150,208)
(151,207)(152,206)(153,205)(154,204)(155,203)(156,202)(157,212)(158,222)
(159,221)(160,220)(161,219)(162,218)(163,217)(164,216)(165,215)(166,214)
(167,213);;
s2 := (  3,114)(  4,113)(  5,123)(  6,122)(  7,121)(  8,120)(  9,119)( 10,118)
( 11,117)( 12,116)( 13,115)( 14,158)( 15,157)( 16,167)( 17,166)( 18,165)
( 19,164)( 20,163)( 21,162)( 22,161)( 23,160)( 24,159)( 25,147)( 26,146)
( 27,156)( 28,155)( 29,154)( 30,153)( 31,152)( 32,151)( 33,150)( 34,149)
( 35,148)( 36,136)( 37,135)( 38,145)( 39,144)( 40,143)( 41,142)( 42,141)
( 43,140)( 44,139)( 45,138)( 46,137)( 47,125)( 48,124)( 49,134)( 50,133)
( 51,132)( 52,131)( 53,130)( 54,129)( 55,128)( 56,127)( 57,126)( 58,169)
( 59,168)( 60,178)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)( 66,172)
( 67,171)( 68,170)( 69,213)( 70,212)( 71,222)( 72,221)( 73,220)( 74,219)
( 75,218)( 76,217)( 77,216)( 78,215)( 79,214)( 80,202)( 81,201)( 82,211)
( 83,210)( 84,209)( 85,208)( 86,207)( 87,206)( 88,205)( 89,204)( 90,203)
( 91,191)( 92,190)( 93,200)( 94,199)( 95,198)( 96,197)( 97,196)( 98,195)
( 99,194)(100,193)(101,192)(102,180)(103,179)(104,189)(105,188)(106,187)
(107,186)(108,185)(109,184)(110,183)(111,182)(112,181);;
s3 := (  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)( 10, 21)
( 11, 22)( 12, 23)( 13, 24)( 25, 47)( 26, 48)( 27, 49)( 28, 50)( 29, 51)
( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 34, 56)( 35, 57)( 58, 69)( 59, 70)
( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)( 67, 78)
( 68, 79)( 80,102)( 81,103)( 82,104)( 83,105)( 84,106)( 85,107)( 86,108)
( 87,109)( 88,110)( 89,111)( 90,112)(113,124)(114,125)(115,126)(116,127)
(117,128)(118,129)(119,130)(120,131)(121,132)(122,133)(123,134)(135,157)
(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)
(144,166)(145,167)(168,179)(169,180)(170,181)(171,182)(172,183)(173,184)
(174,185)(175,186)(176,187)(177,188)(178,189)(190,212)(191,213)(192,214)
(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(199,221)(200,222);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(222)!(1,2);
s1 := Sym(222)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)
( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)
( 85, 86)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)
(105,110)(106,109)(107,108)(113,168)(114,178)(115,177)(116,176)(117,175)
(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)(124,179)(125,189)
(126,188)(127,187)(128,186)(129,185)(130,184)(131,183)(132,182)(133,181)
(134,180)(135,190)(136,200)(137,199)(138,198)(139,197)(140,196)(141,195)
(142,194)(143,193)(144,192)(145,191)(146,201)(147,211)(148,210)(149,209)
(150,208)(151,207)(152,206)(153,205)(154,204)(155,203)(156,202)(157,212)
(158,222)(159,221)(160,220)(161,219)(162,218)(163,217)(164,216)(165,215)
(166,214)(167,213);
s2 := Sym(222)!(  3,114)(  4,113)(  5,123)(  6,122)(  7,121)(  8,120)(  9,119)
( 10,118)( 11,117)( 12,116)( 13,115)( 14,158)( 15,157)( 16,167)( 17,166)
( 18,165)( 19,164)( 20,163)( 21,162)( 22,161)( 23,160)( 24,159)( 25,147)
( 26,146)( 27,156)( 28,155)( 29,154)( 30,153)( 31,152)( 32,151)( 33,150)
( 34,149)( 35,148)( 36,136)( 37,135)( 38,145)( 39,144)( 40,143)( 41,142)
( 42,141)( 43,140)( 44,139)( 45,138)( 46,137)( 47,125)( 48,124)( 49,134)
( 50,133)( 51,132)( 52,131)( 53,130)( 54,129)( 55,128)( 56,127)( 57,126)
( 58,169)( 59,168)( 60,178)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)
( 66,172)( 67,171)( 68,170)( 69,213)( 70,212)( 71,222)( 72,221)( 73,220)
( 74,219)( 75,218)( 76,217)( 77,216)( 78,215)( 79,214)( 80,202)( 81,201)
( 82,211)( 83,210)( 84,209)( 85,208)( 86,207)( 87,206)( 88,205)( 89,204)
( 90,203)( 91,191)( 92,190)( 93,200)( 94,199)( 95,198)( 96,197)( 97,196)
( 98,195)( 99,194)(100,193)(101,192)(102,180)(103,179)(104,189)(105,188)
(106,187)(107,186)(108,185)(109,184)(110,183)(111,182)(112,181);
s3 := Sym(222)!(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)
( 10, 21)( 11, 22)( 12, 23)( 13, 24)( 25, 47)( 26, 48)( 27, 49)( 28, 50)
( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 34, 56)( 35, 57)( 58, 69)
( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)
( 67, 78)( 68, 79)( 80,102)( 81,103)( 82,104)( 83,105)( 84,106)( 85,107)
( 86,108)( 87,109)( 88,110)( 89,111)( 90,112)(113,124)(114,125)(115,126)
(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(122,133)(123,134)
(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)
(143,165)(144,166)(145,167)(168,179)(169,180)(170,181)(171,182)(172,183)
(173,184)(174,185)(175,186)(176,187)(177,188)(178,189)(190,212)(191,213)
(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(199,221)
(200,222);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 

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