Polytope of Type {2,22,20}

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

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

to this polytope