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Polytope of Type {228,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {228,2,2}*1824
if this polytope has a name.
Group : SmallGroup(1824,1226)
Rank : 4
Schlafli Type : {228,2,2}
Number of vertices, edges, etc : 228, 228, 2, 2
Order of s0s1s2s3 : 228
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 : {114,2,2}*912
   3-fold quotients : {76,2,2}*608
   4-fold quotients : {57,2,2}*456
   6-fold quotients : {38,2,2}*304
   12-fold quotients : {19,2,2}*152
   19-fold quotients : {12,2,2}*96
   38-fold quotients : {6,2,2}*48
   57-fold quotients : {4,2,2}*32
   76-fold quotients : {3,2,2}*24
   114-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)( 26, 52)
( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)( 34, 44)
( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)
( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)
( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)
(115,172)(116,190)(117,189)(118,188)(119,187)(120,186)(121,185)(122,184)
(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)(130,176)
(131,175)(132,174)(133,173)(134,210)(135,228)(136,227)(137,226)(138,225)
(139,224)(140,223)(141,222)(142,221)(143,220)(144,219)(145,218)(146,217)
(147,216)(148,215)(149,214)(150,213)(151,212)(152,211)(153,191)(154,209)
(155,208)(156,207)(157,206)(158,205)(159,204)(160,203)(161,202)(162,201)
(163,200)(164,199)(165,198)(166,197)(167,196)(168,195)(169,194)(170,193)
(171,192);;
s1 := (  1,135)(  2,134)(  3,152)(  4,151)(  5,150)(  6,149)(  7,148)(  8,147)
(  9,146)( 10,145)( 11,144)( 12,143)( 13,142)( 14,141)( 15,140)( 16,139)
( 17,138)( 18,137)( 19,136)( 20,116)( 21,115)( 22,133)( 23,132)( 24,131)
( 25,130)( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)( 32,123)
( 33,122)( 34,121)( 35,120)( 36,119)( 37,118)( 38,117)( 39,154)( 40,153)
( 41,171)( 42,170)( 43,169)( 44,168)( 45,167)( 46,166)( 47,165)( 48,164)
( 49,163)( 50,162)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)( 56,156)
( 57,155)( 58,192)( 59,191)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)
( 65,204)( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)( 72,197)
( 73,196)( 74,195)( 75,194)( 76,193)( 77,173)( 78,172)( 79,190)( 80,189)
( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)( 88,181)
( 89,180)( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174)( 96,211)
( 97,210)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,223)(104,222)
(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)
(113,213)(114,212);;
s2 := (229,230);;
s3 := (231,232);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(232)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)
( 26, 52)( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)
( 34, 44)( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)
( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)
( 79,113)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)
( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)
( 95, 97)(115,172)(116,190)(117,189)(118,188)(119,187)(120,186)(121,185)
(122,184)(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)
(130,176)(131,175)(132,174)(133,173)(134,210)(135,228)(136,227)(137,226)
(138,225)(139,224)(140,223)(141,222)(142,221)(143,220)(144,219)(145,218)
(146,217)(147,216)(148,215)(149,214)(150,213)(151,212)(152,211)(153,191)
(154,209)(155,208)(156,207)(157,206)(158,205)(159,204)(160,203)(161,202)
(162,201)(163,200)(164,199)(165,198)(166,197)(167,196)(168,195)(169,194)
(170,193)(171,192);
s1 := Sym(232)!(  1,135)(  2,134)(  3,152)(  4,151)(  5,150)(  6,149)(  7,148)
(  8,147)(  9,146)( 10,145)( 11,144)( 12,143)( 13,142)( 14,141)( 15,140)
( 16,139)( 17,138)( 18,137)( 19,136)( 20,116)( 21,115)( 22,133)( 23,132)
( 24,131)( 25,130)( 26,129)( 27,128)( 28,127)( 29,126)( 30,125)( 31,124)
( 32,123)( 33,122)( 34,121)( 35,120)( 36,119)( 37,118)( 38,117)( 39,154)
( 40,153)( 41,171)( 42,170)( 43,169)( 44,168)( 45,167)( 46,166)( 47,165)
( 48,164)( 49,163)( 50,162)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,156)( 57,155)( 58,192)( 59,191)( 60,209)( 61,208)( 62,207)( 63,206)
( 64,205)( 65,204)( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)
( 72,197)( 73,196)( 74,195)( 75,194)( 76,193)( 77,173)( 78,172)( 79,190)
( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)
( 88,181)( 89,180)( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174)
( 96,211)( 97,210)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,223)
(104,222)(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)
(112,214)(113,213)(114,212);
s2 := Sym(232)!(229,230);
s3 := Sym(232)!(231,232);
poly := sub<Sym(232)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*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*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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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