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Polytope of Type {2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 4
Schlafli Type : {2,20,6}
Number of vertices, edges, etc : 2, 80, 240, 24
Order of s0s1s2s3 : 60
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 : {2,20,6}*960c
   4-fold quotients : {2,20,6}*480a, {2,20,6}*480b
   5-fold quotients : {2,4,6}*384b
   8-fold quotients : {2,10,6}*240
   10-fold quotients : {2,4,6}*192
   12-fold quotients : {2,20,2}*160
   20-fold quotients : {2,4,6}*96a, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {2,4,3}*48, {2,2,6}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,4,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7, 21)(  8, 22)(  9, 19)( 10, 20)( 11, 17)( 12, 18)
( 13, 15)( 14, 16)( 23, 25)( 24, 26)( 27, 41)( 28, 42)( 29, 39)( 30, 40)
( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 43, 45)( 44, 46)( 47, 61)( 48, 62)
( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 63, 65)( 64, 66)
( 67, 81)( 68, 82)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)( 74, 76)
( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)( 92, 98)
( 93, 95)( 94, 96)(103,105)(104,106)(107,121)(108,122)(109,119)(110,120)
(111,117)(112,118)(113,115)(114,116)(123,185)(124,186)(125,183)(126,184)
(127,201)(128,202)(129,199)(130,200)(131,197)(132,198)(133,195)(134,196)
(135,193)(136,194)(137,191)(138,192)(139,189)(140,190)(141,187)(142,188)
(143,205)(144,206)(145,203)(146,204)(147,221)(148,222)(149,219)(150,220)
(151,217)(152,218)(153,215)(154,216)(155,213)(156,214)(157,211)(158,212)
(159,209)(160,210)(161,207)(162,208)(163,225)(164,226)(165,223)(166,224)
(167,241)(168,242)(169,239)(170,240)(171,237)(172,238)(173,235)(174,236)
(175,233)(176,234)(177,231)(178,232)(179,229)(180,230)(181,227)(182,228);;
s2 := (  3,127)(  4,129)(  5,128)(  6,130)(  7,123)(  8,125)(  9,124)( 10,126)
( 11,139)( 12,141)( 13,140)( 14,142)( 15,135)( 16,137)( 17,136)( 18,138)
( 19,131)( 20,133)( 21,132)( 22,134)( 23,167)( 24,169)( 25,168)( 26,170)
( 27,163)( 28,165)( 29,164)( 30,166)( 31,179)( 32,181)( 33,180)( 34,182)
( 35,175)( 36,177)( 37,176)( 38,178)( 39,171)( 40,173)( 41,172)( 42,174)
( 43,147)( 44,149)( 45,148)( 46,150)( 47,143)( 48,145)( 49,144)( 50,146)
( 51,159)( 52,161)( 53,160)( 54,162)( 55,155)( 56,157)( 57,156)( 58,158)
( 59,151)( 60,153)( 61,152)( 62,154)( 63,187)( 64,189)( 65,188)( 66,190)
( 67,183)( 68,185)( 69,184)( 70,186)( 71,199)( 72,201)( 73,200)( 74,202)
( 75,195)( 76,197)( 77,196)( 78,198)( 79,191)( 80,193)( 81,192)( 82,194)
( 83,227)( 84,229)( 85,228)( 86,230)( 87,223)( 88,225)( 89,224)( 90,226)
( 91,239)( 92,241)( 93,240)( 94,242)( 95,235)( 96,237)( 97,236)( 98,238)
( 99,231)(100,233)(101,232)(102,234)(103,207)(104,209)(105,208)(106,210)
(107,203)(108,205)(109,204)(110,206)(111,219)(112,221)(113,220)(114,222)
(115,215)(116,217)(117,216)(118,218)(119,211)(120,213)(121,212)(122,214);;
s3 := (  3, 43)(  4, 46)(  5, 45)(  6, 44)(  7, 47)(  8, 50)(  9, 49)( 10, 48)
( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 59)( 20, 62)( 21, 61)( 22, 60)( 24, 26)( 28, 30)( 32, 34)( 36, 38)
( 40, 42)( 63,103)( 64,106)( 65,105)( 66,104)( 67,107)( 68,110)( 69,109)
( 70,108)( 71,111)( 72,114)( 73,113)( 74,112)( 75,115)( 76,118)( 77,117)
( 78,116)( 79,119)( 80,122)( 81,121)( 82,120)( 84, 86)( 88, 90)( 92, 94)
( 96, 98)(100,102)(123,163)(124,166)(125,165)(126,164)(127,167)(128,170)
(129,169)(130,168)(131,171)(132,174)(133,173)(134,172)(135,175)(136,178)
(137,177)(138,176)(139,179)(140,182)(141,181)(142,180)(144,146)(148,150)
(152,154)(156,158)(160,162)(183,223)(184,226)(185,225)(186,224)(187,227)
(188,230)(189,229)(190,228)(191,231)(192,234)(193,233)(194,232)(195,235)
(196,238)(197,237)(198,236)(199,239)(200,242)(201,241)(202,240)(204,206)
(208,210)(212,214)(216,218)(220,222);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*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(242)!(1,2);
s1 := Sym(242)!(  3,  5)(  4,  6)(  7, 21)(  8, 22)(  9, 19)( 10, 20)( 11, 17)
( 12, 18)( 13, 15)( 14, 16)( 23, 25)( 24, 26)( 27, 41)( 28, 42)( 29, 39)
( 30, 40)( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 43, 45)( 44, 46)( 47, 61)
( 48, 62)( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 63, 65)
( 64, 66)( 67, 81)( 68, 82)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)
( 74, 76)( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)
( 92, 98)( 93, 95)( 94, 96)(103,105)(104,106)(107,121)(108,122)(109,119)
(110,120)(111,117)(112,118)(113,115)(114,116)(123,185)(124,186)(125,183)
(126,184)(127,201)(128,202)(129,199)(130,200)(131,197)(132,198)(133,195)
(134,196)(135,193)(136,194)(137,191)(138,192)(139,189)(140,190)(141,187)
(142,188)(143,205)(144,206)(145,203)(146,204)(147,221)(148,222)(149,219)
(150,220)(151,217)(152,218)(153,215)(154,216)(155,213)(156,214)(157,211)
(158,212)(159,209)(160,210)(161,207)(162,208)(163,225)(164,226)(165,223)
(166,224)(167,241)(168,242)(169,239)(170,240)(171,237)(172,238)(173,235)
(174,236)(175,233)(176,234)(177,231)(178,232)(179,229)(180,230)(181,227)
(182,228);
s2 := Sym(242)!(  3,127)(  4,129)(  5,128)(  6,130)(  7,123)(  8,125)(  9,124)
( 10,126)( 11,139)( 12,141)( 13,140)( 14,142)( 15,135)( 16,137)( 17,136)
( 18,138)( 19,131)( 20,133)( 21,132)( 22,134)( 23,167)( 24,169)( 25,168)
( 26,170)( 27,163)( 28,165)( 29,164)( 30,166)( 31,179)( 32,181)( 33,180)
( 34,182)( 35,175)( 36,177)( 37,176)( 38,178)( 39,171)( 40,173)( 41,172)
( 42,174)( 43,147)( 44,149)( 45,148)( 46,150)( 47,143)( 48,145)( 49,144)
( 50,146)( 51,159)( 52,161)( 53,160)( 54,162)( 55,155)( 56,157)( 57,156)
( 58,158)( 59,151)( 60,153)( 61,152)( 62,154)( 63,187)( 64,189)( 65,188)
( 66,190)( 67,183)( 68,185)( 69,184)( 70,186)( 71,199)( 72,201)( 73,200)
( 74,202)( 75,195)( 76,197)( 77,196)( 78,198)( 79,191)( 80,193)( 81,192)
( 82,194)( 83,227)( 84,229)( 85,228)( 86,230)( 87,223)( 88,225)( 89,224)
( 90,226)( 91,239)( 92,241)( 93,240)( 94,242)( 95,235)( 96,237)( 97,236)
( 98,238)( 99,231)(100,233)(101,232)(102,234)(103,207)(104,209)(105,208)
(106,210)(107,203)(108,205)(109,204)(110,206)(111,219)(112,221)(113,220)
(114,222)(115,215)(116,217)(117,216)(118,218)(119,211)(120,213)(121,212)
(122,214);
s3 := Sym(242)!(  3, 43)(  4, 46)(  5, 45)(  6, 44)(  7, 47)(  8, 50)(  9, 49)
( 10, 48)( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 59)( 20, 62)( 21, 61)( 22, 60)( 24, 26)( 28, 30)( 32, 34)
( 36, 38)( 40, 42)( 63,103)( 64,106)( 65,105)( 66,104)( 67,107)( 68,110)
( 69,109)( 70,108)( 71,111)( 72,114)( 73,113)( 74,112)( 75,115)( 76,118)
( 77,117)( 78,116)( 79,119)( 80,122)( 81,121)( 82,120)( 84, 86)( 88, 90)
( 92, 94)( 96, 98)(100,102)(123,163)(124,166)(125,165)(126,164)(127,167)
(128,170)(129,169)(130,168)(131,171)(132,174)(133,173)(134,172)(135,175)
(136,178)(137,177)(138,176)(139,179)(140,182)(141,181)(142,180)(144,146)
(148,150)(152,154)(156,158)(160,162)(183,223)(184,226)(185,225)(186,224)
(187,227)(188,230)(189,229)(190,228)(191,231)(192,234)(193,233)(194,232)
(195,235)(196,238)(197,237)(198,236)(199,239)(200,242)(201,241)(202,240)
(204,206)(208,210)(212,214)(216,218)(220,222);
poly := sub<Sym(242)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*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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