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Polytope of Type {2,6,20}

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

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