Polytope of Type {4,22}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,22}*1936
Also Known As : {4,22}4. if this polytope has another name.
Group : SmallGroup(1936,161)
Rank : 3
Schlafli Type : {4,22}
Number of vertices, edges, etc : 44, 484, 242
Order of s0s1s2 : 4
Order of s0s1s2s1 : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,22}*968
   121-fold quotients : {4,2}*16
   242-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      121 facets:
         121 of {4}*8
      23 vertex figures:
         21 of {22}*44
         2 of {11}*22
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 11.
      22 facets:
         22 of {4}*8
      4 vertex figures:
         4 of {22}*44
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 11.
      22 facets:
         22 of {4}*8
      4 vertex figures:
         4 of {22}*44
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 11.
      22 facets:
         22 of {4}*8
      4 vertex figures:
         4 of {22}*44
   P/N, where N=<s0*s1*s2*s1*s0*s2> of order 11.
      22 facets:
         22 of {4}*8
      24 vertex figures:
         2 of {22}*44
         22 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 22.
      11 facets:
         11 of {4}*8
      13 vertex figures:
         2 of {11}*22
         11 of {2}*4

Permutation Representation (GAP) : 
s0 := (  2,112)(  3,102)(  4, 92)(  5, 82)(  6, 72)(  7, 62)(  8, 52)(  9, 42)( 10, 32)( 11, 22)( 12,111)( 13,101)( 14, 91)( 15, 81)( 16, 71)( 17, 61)( 18, 51)( 19, 41)( 20, 31)( 23,100)( 24, 90)( 25, 80)( 26, 70)( 27, 60)( 28, 50)( 29, 40)( 33,121)( 34, 89)( 35, 79)( 36, 69)( 37, 59)( 38, 49)( 43,120)( 44,110)( 45, 78)( 46, 68)( 47, 58)( 53,119)( 54,109)( 55, 99)( 56, 67)( 63,118)( 64,108)( 65, 98)( 66, 88)( 73,117)( 74,107)( 75, 97)( 76, 87)( 83,116)( 84,106)( 85, 96)( 93,115)( 94,105)(103,114)(123,233)(124,223)(125,213)(126,203)(127,193)(128,183)(129,173)(130,163)(131,153)(132,143)(133,232)(134,222)(135,212)(136,202)(137,192)(138,182)(139,172)(140,162)(141,152)(144,221)(145,211)(146,201)(147,191)(148,181)(149,171)(150,161)(154,242)(155,210)(156,200)(157,190)(158,180)(159,170)(164,241)(165,231)(166,199)(167,189)(168,179)(174,240)(175,230)(176,220)(177,188)(184,239)(185,229)(186,219)(187,209)(194,238)(195,228)(196,218)(197,208)(204,237)(205,227)(206,217)(214,236)(215,226)(224,235);;
s1 := ( 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);;
s2 := (  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)(  9,181)( 10,180)( 11,179)( 12,167)( 13,166)( 14,176)( 15,175)( 16,174)( 17,173)( 18,172)( 19,171)( 20,170)( 21,169)( 22,168)( 23,156)( 24,155)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)( 33,157)( 34,145)( 35,144)( 36,154)( 37,153)( 38,152)( 39,151)( 40,150)( 41,149)( 42,148)( 43,147)( 44,146)( 45,134)( 46,133)( 47,143)( 48,142)( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)( 56,123)( 57,122)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)( 65,125)( 66,124)( 67,233)( 68,232)( 69,242)( 70,241)( 71,240)( 72,239)( 73,238)( 74,237)( 75,236)( 76,235)( 77,234)( 78,222)( 79,221)( 80,231)( 81,230)( 82,229)( 83,228)( 84,227)( 85,226)( 86,225)( 87,224)( 88,223)( 89,211)( 90,210)( 91,220)( 92,219)( 93,218)( 94,217)( 95,216)( 96,215)( 97,214)( 98,213)( 99,212)(100,200)(101,199)(102,209)(103,208)(104,207)(105,206)(106,205)(107,204)(108,203)(109,202)(110,201)(111,189)(112,188)(113,198)(114,197)(115,196)(116,195)(117,194)(118,193)(119,192)(120,191)(121,190);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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(242)!(  2,112)(  3,102)(  4, 92)(  5, 82)(  6, 72)(  7, 62)(  8, 52)(  9, 42)( 10, 32)( 11, 22)( 12,111)( 13,101)( 14, 91)( 15, 81)( 16, 71)( 17, 61)( 18, 51)( 19, 41)( 20, 31)( 23,100)( 24, 90)( 25, 80)( 26, 70)( 27, 60)( 28, 50)( 29, 40)( 33,121)( 34, 89)( 35, 79)( 36, 69)( 37, 59)( 38, 49)( 43,120)( 44,110)( 45, 78)( 46, 68)( 47, 58)( 53,119)( 54,109)( 55, 99)( 56, 67)( 63,118)( 64,108)( 65, 98)( 66, 88)( 73,117)( 74,107)( 75, 97)( 76, 87)( 83,116)( 84,106)( 85, 96)( 93,115)( 94,105)(103,114)(123,233)(124,223)(125,213)(126,203)(127,193)(128,183)(129,173)(130,163)(131,153)(132,143)(133,232)(134,222)(135,212)(136,202)(137,192)(138,182)(139,172)(140,162)(141,152)(144,221)(145,211)(146,201)(147,191)(148,181)(149,171)(150,161)(154,242)(155,210)(156,200)(157,190)(158,180)(159,170)(164,241)(165,231)(166,199)(167,189)(168,179)(174,240)(175,230)(176,220)(177,188)(184,239)(185,229)(186,219)(187,209)(194,238)(195,228)(196,218)(197,208)(204,237)(205,227)(206,217)(214,236)(215,226)(224,235);
s1 := 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);
s2 := Sym(242)!(  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)(  9,181)( 10,180)( 11,179)( 12,167)( 13,166)( 14,176)( 15,175)( 16,174)( 17,173)( 18,172)( 19,171)( 20,170)( 21,169)( 22,168)( 23,156)( 24,155)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)( 33,157)( 34,145)( 35,144)( 36,154)( 37,153)( 38,152)( 39,151)( 40,150)( 41,149)( 42,148)( 43,147)( 44,146)( 45,134)( 46,133)( 47,143)( 48,142)( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)( 56,123)( 57,122)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)( 65,125)( 66,124)( 67,233)( 68,232)( 69,242)( 70,241)( 71,240)( 72,239)( 73,238)( 74,237)( 75,236)( 76,235)( 77,234)( 78,222)( 79,221)( 80,231)( 81,230)( 82,229)( 83,228)( 84,227)( 85,226)( 86,225)( 87,224)( 88,223)( 89,211)( 90,210)( 91,220)( 92,219)( 93,218)( 94,217)( 95,216)( 96,215)( 97,214)( 98,213)( 99,212)(100,200)(101,199)(102,209)(103,208)(104,207)(105,206)(106,205)(107,204)(108,203)(109,202)(110,201)(111,189)(112,188)(113,198)(114,197)(115,196)(116,195)(117,194)(118,193)(119,192)(120,191)(121,190);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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 >;
References : None.
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