Polytope of Type {44,10}

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

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