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Polytope of Type {20,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,3}*960
Also Known As : {{20,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(960,10952)
Rank : 4
Schlafli Type : {20,4,3}
Number of vertices, edges, etc : 20, 80, 12, 6
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,4,3,2} of size 1920
Vertex Figure Of :
   {2,20,4,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,4,3}*480
   4-fold quotients : {20,2,3}*240
   5-fold quotients : {4,4,3}*192b
   8-fold quotients : {10,2,3}*120
   10-fold quotients : {2,4,3}*96
   16-fold quotients : {5,2,3}*60
   20-fold quotients : {4,2,3}*48, {2,4,3}*48
   40-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,8,3}*1920, {40,4,3}*1920, {20,4,6}*1920b
Permutation Representation (GAP) :
s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)
(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)(128,200)
(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)(136,192)
(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)(144,204)
(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)(152,216)
(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)(160,208)
(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)(168,240)
(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)(176,232)
(177,225)(178,226)(179,227)(180,228);;
s1 := (  1,127)(  2,128)(  3,125)(  4,126)(  5,123)(  6,124)(  7,121)(  8,122)
(  9,139)( 10,140)( 11,137)( 12,138)( 13,135)( 14,136)( 15,133)( 16,134)
( 17,131)( 18,132)( 19,129)( 20,130)( 21,147)( 22,148)( 23,145)( 24,146)
( 25,143)( 26,144)( 27,141)( 28,142)( 29,159)( 30,160)( 31,157)( 32,158)
( 33,155)( 34,156)( 35,153)( 36,154)( 37,151)( 38,152)( 39,149)( 40,150)
( 41,167)( 42,168)( 43,165)( 44,166)( 45,163)( 46,164)( 47,161)( 48,162)
( 49,179)( 50,180)( 51,177)( 52,178)( 53,175)( 54,176)( 55,173)( 56,174)
( 57,171)( 58,172)( 59,169)( 60,170)( 61,187)( 62,188)( 63,185)( 64,186)
( 65,183)( 66,184)( 67,181)( 68,182)( 69,199)( 70,200)( 71,197)( 72,198)
( 73,195)( 74,196)( 75,193)( 76,194)( 77,191)( 78,192)( 79,189)( 80,190)
( 81,207)( 82,208)( 83,205)( 84,206)( 85,203)( 86,204)( 87,201)( 88,202)
( 89,219)( 90,220)( 91,217)( 92,218)( 93,215)( 94,216)( 95,213)( 96,214)
( 97,211)( 98,212)( 99,209)(100,210)(101,227)(102,228)(103,225)(104,226)
(105,223)(106,224)(107,221)(108,222)(109,239)(110,240)(111,237)(112,238)
(113,235)(114,236)(115,233)(116,234)(117,231)(118,232)(119,229)(120,230);;
s2 := (  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120)(122,123)(126,127)(130,131)(134,135)(138,139)(141,161)
(142,163)(143,162)(144,164)(145,165)(146,167)(147,166)(148,168)(149,169)
(150,171)(151,170)(152,172)(153,173)(154,175)(155,174)(156,176)(157,177)
(158,179)(159,178)(160,180)(182,183)(186,187)(190,191)(194,195)(198,199)
(201,221)(202,223)(203,222)(204,224)(205,225)(206,227)(207,226)(208,228)
(209,229)(210,231)(211,230)(212,232)(213,233)(214,235)(215,234)(216,236)
(217,237)(218,239)(219,238)(220,240);;
s3 := (  1, 41)(  2, 44)(  3, 43)(  4, 42)(  5, 45)(  6, 48)(  7, 47)(  8, 46)
(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 22, 24)( 26, 28)( 30, 32)( 34, 36)
( 38, 40)( 61,101)( 62,104)( 63,103)( 64,102)( 65,105)( 66,108)( 67,107)
( 68,106)( 69,109)( 70,112)( 71,111)( 72,110)( 73,113)( 74,116)( 75,115)
( 76,114)( 77,117)( 78,120)( 79,119)( 80,118)( 82, 84)( 86, 88)( 90, 92)
( 94, 96)( 98,100)(121,161)(122,164)(123,163)(124,162)(125,165)(126,168)
(127,167)(128,166)(129,169)(130,172)(131,171)(132,170)(133,173)(134,176)
(135,175)(136,174)(137,177)(138,180)(139,179)(140,178)(142,144)(146,148)
(150,152)(154,156)(158,160)(181,221)(182,224)(183,223)(184,222)(185,225)
(186,228)(187,227)(188,226)(189,229)(190,232)(191,231)(192,230)(193,233)
(194,236)(195,235)(196,234)(197,237)(198,240)(199,239)(200,238)(202,204)
(206,208)(210,212)(214,216)(218,220);;
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*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(240)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116)(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)
(128,200)(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)
(136,192)(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)
(144,204)(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)
(152,216)(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)
(160,208)(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)
(168,240)(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)
(176,232)(177,225)(178,226)(179,227)(180,228);
s1 := Sym(240)!(  1,127)(  2,128)(  3,125)(  4,126)(  5,123)(  6,124)(  7,121)
(  8,122)(  9,139)( 10,140)( 11,137)( 12,138)( 13,135)( 14,136)( 15,133)
( 16,134)( 17,131)( 18,132)( 19,129)( 20,130)( 21,147)( 22,148)( 23,145)
( 24,146)( 25,143)( 26,144)( 27,141)( 28,142)( 29,159)( 30,160)( 31,157)
( 32,158)( 33,155)( 34,156)( 35,153)( 36,154)( 37,151)( 38,152)( 39,149)
( 40,150)( 41,167)( 42,168)( 43,165)( 44,166)( 45,163)( 46,164)( 47,161)
( 48,162)( 49,179)( 50,180)( 51,177)( 52,178)( 53,175)( 54,176)( 55,173)
( 56,174)( 57,171)( 58,172)( 59,169)( 60,170)( 61,187)( 62,188)( 63,185)
( 64,186)( 65,183)( 66,184)( 67,181)( 68,182)( 69,199)( 70,200)( 71,197)
( 72,198)( 73,195)( 74,196)( 75,193)( 76,194)( 77,191)( 78,192)( 79,189)
( 80,190)( 81,207)( 82,208)( 83,205)( 84,206)( 85,203)( 86,204)( 87,201)
( 88,202)( 89,219)( 90,220)( 91,217)( 92,218)( 93,215)( 94,216)( 95,213)
( 96,214)( 97,211)( 98,212)( 99,209)(100,210)(101,227)(102,228)(103,225)
(104,226)(105,223)(106,224)(107,221)(108,222)(109,239)(110,240)(111,237)
(112,238)(113,235)(114,236)(115,233)(116,234)(117,231)(118,232)(119,229)
(120,230);
s2 := Sym(240)!(  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)
( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)
( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)
( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)
( 98,119)( 99,118)(100,120)(122,123)(126,127)(130,131)(134,135)(138,139)
(141,161)(142,163)(143,162)(144,164)(145,165)(146,167)(147,166)(148,168)
(149,169)(150,171)(151,170)(152,172)(153,173)(154,175)(155,174)(156,176)
(157,177)(158,179)(159,178)(160,180)(182,183)(186,187)(190,191)(194,195)
(198,199)(201,221)(202,223)(203,222)(204,224)(205,225)(206,227)(207,226)
(208,228)(209,229)(210,231)(211,230)(212,232)(213,233)(214,235)(215,234)
(216,236)(217,237)(218,239)(219,238)(220,240);
s3 := Sym(240)!(  1, 41)(  2, 44)(  3, 43)(  4, 42)(  5, 45)(  6, 48)(  7, 47)
(  8, 46)(  9, 49)( 10, 52)( 11, 51)( 12, 50)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 57)( 18, 60)( 19, 59)( 20, 58)( 22, 24)( 26, 28)( 30, 32)
( 34, 36)( 38, 40)( 61,101)( 62,104)( 63,103)( 64,102)( 65,105)( 66,108)
( 67,107)( 68,106)( 69,109)( 70,112)( 71,111)( 72,110)( 73,113)( 74,116)
( 75,115)( 76,114)( 77,117)( 78,120)( 79,119)( 80,118)( 82, 84)( 86, 88)
( 90, 92)( 94, 96)( 98,100)(121,161)(122,164)(123,163)(124,162)(125,165)
(126,168)(127,167)(128,166)(129,169)(130,172)(131,171)(132,170)(133,173)
(134,176)(135,175)(136,174)(137,177)(138,180)(139,179)(140,178)(142,144)
(146,148)(150,152)(154,156)(158,160)(181,221)(182,224)(183,223)(184,222)
(185,225)(186,228)(187,227)(188,226)(189,229)(190,232)(191,231)(192,230)
(193,233)(194,236)(195,235)(196,234)(197,237)(198,240)(199,239)(200,238)
(202,204)(206,208)(210,212)(214,216)(218,220);
poly := sub<Sym(240)|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*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope