Polytope of Type {22,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4}*1936
Also Known As : {22,4}₄. if this polytope has another name.
Group : SmallGroup(1936,161)
Rank : 3
Schlafli Type : {22,4}
Number of vertices, edges, etc : 242, 484, 44
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,4}*968
   121-fold quotients : {2,4}*16
   242-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,122)(  2,132)(  3,131)(  4,130)(  5,129)(  6,128)(  7,127)(  8,126)
(  9,125)( 10,124)( 11,123)( 12,232)( 13,242)( 14,241)( 15,240)( 16,239)
( 17,238)( 18,237)( 19,236)( 20,235)( 21,234)( 22,233)( 23,221)( 24,231)
( 25,230)( 26,229)( 27,228)( 28,227)( 29,226)( 30,225)( 31,224)( 32,223)
( 33,222)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)( 40,215)
( 41,214)( 42,213)( 43,212)( 44,211)( 45,199)( 46,209)( 47,208)( 48,207)
( 49,206)( 50,205)( 51,204)( 52,203)( 53,202)( 54,201)( 55,200)( 56,188)
( 57,198)( 58,197)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)( 64,191)
( 65,190)( 66,189)( 67,177)( 68,187)( 69,186)( 70,185)( 71,184)( 72,183)
( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,166)( 79,176)( 80,175)
( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)( 88,167)
( 89,155)( 90,165)( 91,164)( 92,163)( 93,162)( 94,161)( 95,160)( 96,159)
( 97,158)( 98,157)( 99,156)(100,144)(101,154)(102,153)(103,152)(104,151)
(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)(111,133)(112,143)
(113,142)(114,141)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)
(121,134);;
s1 := (  1, 12)(  3,113)(  4,103)(  5, 93)(  6, 83)(  7, 73)(  8, 63)(  9, 53)
( 10, 43)( 11, 33)( 13,112)( 14,102)( 15, 92)( 16, 82)( 17, 72)( 18, 62)
( 19, 52)( 20, 42)( 21, 32)( 23,111)( 24,101)( 25, 91)( 26, 81)( 27, 71)
( 28, 61)( 29, 51)( 30, 41)( 34,100)( 35, 90)( 36, 80)( 37, 70)( 38, 60)
( 39, 50)( 44,121)( 45, 89)( 46, 79)( 47, 69)( 48, 59)( 54,120)( 55,110)
( 56, 78)( 57, 68)( 64,119)( 65,109)( 66, 99)( 74,118)( 75,108)( 76, 98)
( 77, 88)( 84,117)( 85,107)( 86, 97)( 94,116)( 95,106)(104,115)(122,133)
(124,234)(125,224)(126,214)(127,204)(128,194)(129,184)(130,174)(131,164)
(132,154)(134,233)(135,223)(136,213)(137,203)(138,193)(139,183)(140,173)
(141,163)(142,153)(144,232)(145,222)(146,212)(147,202)(148,192)(149,182)
(150,172)(151,162)(155,221)(156,211)(157,201)(158,191)(159,181)(160,171)
(165,242)(166,210)(167,200)(168,190)(169,180)(175,241)(176,231)(177,199)
(178,189)(185,240)(186,230)(187,220)(195,239)(196,229)(197,219)(198,209)
(205,238)(206,228)(207,218)(215,237)(216,227)(225,236);;
s2 := ( 12,113)( 13,114)( 14,115)( 15,116)( 16,117)( 17,118)( 18,119)( 19,120)
( 20,121)( 21,111)( 22,112)( 23,104)( 24,105)( 25,106)( 26,107)( 27,108)
( 28,109)( 29,110)( 30,100)( 31,101)( 32,102)( 33,103)( 34, 95)( 35, 96)
( 36, 97)( 37, 98)( 38, 99)( 39, 89)( 40, 90)( 41, 91)( 42, 92)( 43, 93)
( 44, 94)( 45, 86)( 46, 87)( 47, 88)( 48, 78)( 49, 79)( 50, 80)( 51, 81)
( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 77)( 57, 67)( 58, 68)( 59, 69)
( 60, 70)( 61, 71)( 62, 72)( 63, 73)( 64, 74)( 65, 75)( 66, 76)(133,234)
(134,235)(135,236)(136,237)(137,238)(138,239)(139,240)(140,241)(141,242)
(142,232)(143,233)(144,225)(145,226)(146,227)(147,228)(148,229)(149,230)
(150,231)(151,221)(152,222)(153,223)(154,224)(155,216)(156,217)(157,218)
(158,219)(159,220)(160,210)(161,211)(162,212)(163,213)(164,214)(165,215)
(166,207)(167,208)(168,209)(169,199)(170,200)(171,201)(172,202)(173,203)
(174,204)(175,205)(176,206)(177,198)(178,188)(179,189)(180,190)(181,191)
(182,192)(183,193)(184,194)(185,195)(186,196)(187,197);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(242)!(  1,122)(  2,132)(  3,131)(  4,130)(  5,129)(  6,128)(  7,127)
(  8,126)(  9,125)( 10,124)( 11,123)( 12,232)( 13,242)( 14,241)( 15,240)
( 16,239)( 17,238)( 18,237)( 19,236)( 20,235)( 21,234)( 22,233)( 23,221)
( 24,231)( 25,230)( 26,229)( 27,228)( 28,227)( 29,226)( 30,225)( 31,224)
( 32,223)( 33,222)( 34,210)( 35,220)( 36,219)( 37,218)( 38,217)( 39,216)
( 40,215)( 41,214)( 42,213)( 43,212)( 44,211)( 45,199)( 46,209)( 47,208)
( 48,207)( 49,206)( 50,205)( 51,204)( 52,203)( 53,202)( 54,201)( 55,200)
( 56,188)( 57,198)( 58,197)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)
( 64,191)( 65,190)( 66,189)( 67,177)( 68,187)( 69,186)( 70,185)( 71,184)
( 72,183)( 73,182)( 74,181)( 75,180)( 76,179)( 77,178)( 78,166)( 79,176)
( 80,175)( 81,174)( 82,173)( 83,172)( 84,171)( 85,170)( 86,169)( 87,168)
( 88,167)( 89,155)( 90,165)( 91,164)( 92,163)( 93,162)( 94,161)( 95,160)
( 96,159)( 97,158)( 98,157)( 99,156)(100,144)(101,154)(102,153)(103,152)
(104,151)(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)(111,133)
(112,143)(113,142)(114,141)(115,140)(116,139)(117,138)(118,137)(119,136)
(120,135)(121,134);
s1 := Sym(242)!(  1, 12)(  3,113)(  4,103)(  5, 93)(  6, 83)(  7, 73)(  8, 63)
(  9, 53)( 10, 43)( 11, 33)( 13,112)( 14,102)( 15, 92)( 16, 82)( 17, 72)
( 18, 62)( 19, 52)( 20, 42)( 21, 32)( 23,111)( 24,101)( 25, 91)( 26, 81)
( 27, 71)( 28, 61)( 29, 51)( 30, 41)( 34,100)( 35, 90)( 36, 80)( 37, 70)
( 38, 60)( 39, 50)( 44,121)( 45, 89)( 46, 79)( 47, 69)( 48, 59)( 54,120)
( 55,110)( 56, 78)( 57, 68)( 64,119)( 65,109)( 66, 99)( 74,118)( 75,108)
( 76, 98)( 77, 88)( 84,117)( 85,107)( 86, 97)( 94,116)( 95,106)(104,115)
(122,133)(124,234)(125,224)(126,214)(127,204)(128,194)(129,184)(130,174)
(131,164)(132,154)(134,233)(135,223)(136,213)(137,203)(138,193)(139,183)
(140,173)(141,163)(142,153)(144,232)(145,222)(146,212)(147,202)(148,192)
(149,182)(150,172)(151,162)(155,221)(156,211)(157,201)(158,191)(159,181)
(160,171)(165,242)(166,210)(167,200)(168,190)(169,180)(175,241)(176,231)
(177,199)(178,189)(185,240)(186,230)(187,220)(195,239)(196,229)(197,219)
(198,209)(205,238)(206,228)(207,218)(215,237)(216,227)(225,236);
s2 := Sym(242)!( 12,113)( 13,114)( 14,115)( 15,116)( 16,117)( 17,118)( 18,119)
( 19,120)( 20,121)( 21,111)( 22,112)( 23,104)( 24,105)( 25,106)( 26,107)
( 27,108)( 28,109)( 29,110)( 30,100)( 31,101)( 32,102)( 33,103)( 34, 95)
( 35, 96)( 36, 97)( 37, 98)( 38, 99)( 39, 89)( 40, 90)( 41, 91)( 42, 92)
( 43, 93)( 44, 94)( 45, 86)( 46, 87)( 47, 88)( 48, 78)( 49, 79)( 50, 80)
( 51, 81)( 52, 82)( 53, 83)( 54, 84)( 55, 85)( 56, 77)( 57, 67)( 58, 68)
( 59, 69)( 60, 70)( 61, 71)( 62, 72)( 63, 73)( 64, 74)( 65, 75)( 66, 76)
(133,234)(134,235)(135,236)(136,237)(137,238)(138,239)(139,240)(140,241)
(141,242)(142,232)(143,233)(144,225)(145,226)(146,227)(147,228)(148,229)
(149,230)(150,231)(151,221)(152,222)(153,223)(154,224)(155,216)(156,217)
(157,218)(158,219)(159,220)(160,210)(161,211)(162,212)(163,213)(164,214)
(165,215)(166,207)(167,208)(168,209)(169,199)(170,200)(171,201)(172,202)
(173,203)(174,204)(175,205)(176,206)(177,198)(178,188)(179,189)(180,190)
(181,191)(182,192)(183,193)(184,194)(185,195)(186,196)(187,197);
poly := sub<Sym(242)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*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 >;

References : None.
to this polytope