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Polytope of Type {6,76,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,76,2}*1824a
if this polytope has a name.
Group : SmallGroup(1824,1132)
Rank : 4
Schlafli Type : {6,76,2}
Number of vertices, edges, etc : 6, 228, 76, 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 : {6,38,2}*912
   3-fold quotients : {2,76,2}*608
   6-fold quotients : {2,38,2}*304
   12-fold quotients : {2,19,2}*152
   19-fold quotients : {6,4,2}*96a
   38-fold quotients : {6,2,2}*48
   57-fold quotients : {2,4,2}*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 := ( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)
( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)
( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)( 81,100)
( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)( 89,108)
( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)(134,153)(135,154)
(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)(143,162)
(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)(151,170)
(152,171)(191,210)(192,211)(193,212)(194,213)(195,214)(196,215)(197,216)
(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)
(206,225)(207,226)(208,227)(209,228);;
s1 := (  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)(  8, 32)
(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 58, 77)( 59, 95)( 60, 94)( 61, 93)
( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)
( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)( 97,114)
( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)
(115,191)(116,209)(117,208)(118,207)(119,206)(120,205)(121,204)(122,203)
(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)(130,195)
(131,194)(132,193)(133,192)(134,172)(135,190)(136,189)(137,188)(138,187)
(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)
(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,210)(154,228)
(155,227)(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)
(163,219)(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)(170,212)
(171,211);;
s2 := (  1,116)(  2,115)(  3,133)(  4,132)(  5,131)(  6,130)(  7,129)(  8,128)
(  9,127)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,121)( 16,120)
( 17,119)( 18,118)( 19,117)( 20,135)( 21,134)( 22,152)( 23,151)( 24,150)
( 25,149)( 26,148)( 27,147)( 28,146)( 29,145)( 30,144)( 31,143)( 32,142)
( 33,141)( 34,140)( 35,139)( 36,138)( 37,137)( 38,136)( 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)( 58,173)( 59,172)( 60,190)( 61,189)( 62,188)( 63,187)( 64,186)
( 65,185)( 66,184)( 67,183)( 68,182)( 69,181)( 70,180)( 71,179)( 72,178)
( 73,177)( 74,176)( 75,175)( 76,174)( 77,192)( 78,191)( 79,209)( 80,208)
( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)
( 89,199)( 90,198)( 91,197)( 92,196)( 93,195)( 94,194)( 95,193)( 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);;
s3 := (229,230);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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*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*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(230)!( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)
( 27, 46)( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)
( 35, 54)( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)
( 81,100)( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)
( 89,108)( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)(134,153)
(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)
(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)
(151,170)(152,171)(191,210)(192,211)(193,212)(194,213)(195,214)(196,215)
(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)
(205,224)(206,225)(207,226)(208,227)(209,228);
s1 := Sym(230)!(  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)
(  8, 32)(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 40, 57)( 41, 56)( 42, 55)( 43, 54)
( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 58, 77)( 59, 95)( 60, 94)
( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)
( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)
( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)
(105,106)(115,191)(116,209)(117,208)(118,207)(119,206)(120,205)(121,204)
(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)
(130,195)(131,194)(132,193)(133,192)(134,172)(135,190)(136,189)(137,188)
(138,187)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)
(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,210)
(154,228)(155,227)(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)
(162,220)(163,219)(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)
(170,212)(171,211);
s2 := Sym(230)!(  1,116)(  2,115)(  3,133)(  4,132)(  5,131)(  6,130)(  7,129)
(  8,128)(  9,127)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,121)
( 16,120)( 17,119)( 18,118)( 19,117)( 20,135)( 21,134)( 22,152)( 23,151)
( 24,150)( 25,149)( 26,148)( 27,147)( 28,146)( 29,145)( 30,144)( 31,143)
( 32,142)( 33,141)( 34,140)( 35,139)( 36,138)( 37,137)( 38,136)( 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)( 58,173)( 59,172)( 60,190)( 61,189)( 62,188)( 63,187)
( 64,186)( 65,185)( 66,184)( 67,183)( 68,182)( 69,181)( 70,180)( 71,179)
( 72,178)( 73,177)( 74,176)( 75,175)( 76,174)( 77,192)( 78,191)( 79,209)
( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)
( 88,200)( 89,199)( 90,198)( 91,197)( 92,196)( 93,195)( 94,194)( 95,193)
( 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);
s3 := Sym(230)!(229,230);
poly := sub<Sym(230)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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