Polytope of Type {2,20,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,22}*1760
if this polytope has a name.
Group : SmallGroup(1760,1180)
Rank : 4
Schlafli Type : {2,20,22}
Number of vertices, edges, etc : 2, 20, 220, 22
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 : {2,4,22}*352
   10-fold quotients : {2,2,22}*176
   11-fold quotients : {2,20,2}*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 : {2,4,2}*32
   110-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope