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Polytope of Type {20,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,3}*960
Also Known As : {{20,6|2},{6,3}4}. if this polytope has another name.
Group : SmallGroup(960,10952)
Rank : 4
Schlafli Type : {20,6,3}
Number of vertices, edges, etc : 20, 80, 12, 4
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,6,3,2} of size 1920
Vertex Figure Of :
   {2,20,6,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6,3}*480
   5-fold quotients : {4,6,3}*192
   10-fold quotients : {2,6,3}*96
   20-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,12,3}*1920, {40,6,3}*1920, {20,6,6}*1920
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 := (  1,125)(  2,127)(  3,126)(  4,128)(  5,121)(  6,123)(  7,122)(  8,124)
(  9,137)( 10,139)( 11,138)( 12,140)( 13,133)( 14,135)( 15,134)( 16,136)
( 17,129)( 18,131)( 19,130)( 20,132)( 21,165)( 22,167)( 23,166)( 24,168)
( 25,161)( 26,163)( 27,162)( 28,164)( 29,177)( 30,179)( 31,178)( 32,180)
( 33,173)( 34,175)( 35,174)( 36,176)( 37,169)( 38,171)( 39,170)( 40,172)
( 41,145)( 42,147)( 43,146)( 44,148)( 45,141)( 46,143)( 47,142)( 48,144)
( 49,157)( 50,159)( 51,158)( 52,160)( 53,153)( 54,155)( 55,154)( 56,156)
( 57,149)( 58,151)( 59,150)( 60,152)( 61,185)( 62,187)( 63,186)( 64,188)
( 65,181)( 66,183)( 67,182)( 68,184)( 69,197)( 70,199)( 71,198)( 72,200)
( 73,193)( 74,195)( 75,194)( 76,196)( 77,189)( 78,191)( 79,190)( 80,192)
( 81,225)( 82,227)( 83,226)( 84,228)( 85,221)( 86,223)( 87,222)( 88,224)
( 89,237)( 90,239)( 91,238)( 92,240)( 93,233)( 94,235)( 95,234)( 96,236)
( 97,229)( 98,231)( 99,230)(100,232)(101,205)(102,207)(103,206)(104,208)
(105,201)(106,203)(107,202)(108,204)(109,217)(110,219)(111,218)(112,220)
(113,213)(114,215)(115,214)(116,216)(117,209)(118,211)(119,210)(120,212);;
s2 := (  1, 21)(  2, 22)(  3, 24)(  4, 23)(  5, 25)(  6, 26)(  7, 28)(  8, 27)
(  9, 29)( 10, 30)( 11, 32)( 12, 31)( 13, 33)( 14, 34)( 15, 36)( 16, 35)
( 17, 37)( 18, 38)( 19, 40)( 20, 39)( 43, 44)( 47, 48)( 51, 52)( 55, 56)
( 59, 60)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 85)( 66, 86)( 67, 88)
( 68, 87)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 97)( 78, 98)( 79,100)( 80, 99)(103,104)(107,108)(111,112)
(115,116)(119,120)(121,141)(122,142)(123,144)(124,143)(125,145)(126,146)
(127,148)(128,147)(129,149)(130,150)(131,152)(132,151)(133,153)(134,154)
(135,156)(136,155)(137,157)(138,158)(139,160)(140,159)(163,164)(167,168)
(171,172)(175,176)(179,180)(181,201)(182,202)(183,204)(184,203)(185,205)
(186,206)(187,208)(188,207)(189,209)(190,210)(191,212)(192,211)(193,213)
(194,214)(195,216)(196,215)(197,217)(198,218)(199,220)(200,219)(223,224)
(227,228)(231,232)(235,236)(239,240);;
s3 := (  1,  4)(  5,  8)(  9, 12)( 13, 16)( 17, 20)( 21, 44)( 22, 42)( 23, 43)
( 24, 41)( 25, 48)( 26, 46)( 27, 47)( 28, 45)( 29, 52)( 30, 50)( 31, 51)
( 32, 49)( 33, 56)( 34, 54)( 35, 55)( 36, 53)( 37, 60)( 38, 58)( 39, 59)
( 40, 57)( 61, 64)( 65, 68)( 69, 72)( 73, 76)( 77, 80)( 81,104)( 82,102)
( 83,103)( 84,101)( 85,108)( 86,106)( 87,107)( 88,105)( 89,112)( 90,110)
( 91,111)( 92,109)( 93,116)( 94,114)( 95,115)( 96,113)( 97,120)( 98,118)
( 99,119)(100,117)(121,124)(125,128)(129,132)(133,136)(137,140)(141,164)
(142,162)(143,163)(144,161)(145,168)(146,166)(147,167)(148,165)(149,172)
(150,170)(151,171)(152,169)(153,176)(154,174)(155,175)(156,173)(157,180)
(158,178)(159,179)(160,177)(181,184)(185,188)(189,192)(193,196)(197,200)
(201,224)(202,222)(203,223)(204,221)(205,228)(206,226)(207,227)(208,225)
(209,232)(210,230)(211,231)(212,229)(213,236)(214,234)(215,235)(216,233)
(217,240)(218,238)(219,239)(220,237);;
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*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*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)!(  1,125)(  2,127)(  3,126)(  4,128)(  5,121)(  6,123)(  7,122)
(  8,124)(  9,137)( 10,139)( 11,138)( 12,140)( 13,133)( 14,135)( 15,134)
( 16,136)( 17,129)( 18,131)( 19,130)( 20,132)( 21,165)( 22,167)( 23,166)
( 24,168)( 25,161)( 26,163)( 27,162)( 28,164)( 29,177)( 30,179)( 31,178)
( 32,180)( 33,173)( 34,175)( 35,174)( 36,176)( 37,169)( 38,171)( 39,170)
( 40,172)( 41,145)( 42,147)( 43,146)( 44,148)( 45,141)( 46,143)( 47,142)
( 48,144)( 49,157)( 50,159)( 51,158)( 52,160)( 53,153)( 54,155)( 55,154)
( 56,156)( 57,149)( 58,151)( 59,150)( 60,152)( 61,185)( 62,187)( 63,186)
( 64,188)( 65,181)( 66,183)( 67,182)( 68,184)( 69,197)( 70,199)( 71,198)
( 72,200)( 73,193)( 74,195)( 75,194)( 76,196)( 77,189)( 78,191)( 79,190)
( 80,192)( 81,225)( 82,227)( 83,226)( 84,228)( 85,221)( 86,223)( 87,222)
( 88,224)( 89,237)( 90,239)( 91,238)( 92,240)( 93,233)( 94,235)( 95,234)
( 96,236)( 97,229)( 98,231)( 99,230)(100,232)(101,205)(102,207)(103,206)
(104,208)(105,201)(106,203)(107,202)(108,204)(109,217)(110,219)(111,218)
(112,220)(113,213)(114,215)(115,214)(116,216)(117,209)(118,211)(119,210)
(120,212);
s2 := Sym(240)!(  1, 21)(  2, 22)(  3, 24)(  4, 23)(  5, 25)(  6, 26)(  7, 28)
(  8, 27)(  9, 29)( 10, 30)( 11, 32)( 12, 31)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 37)( 18, 38)( 19, 40)( 20, 39)( 43, 44)( 47, 48)( 51, 52)
( 55, 56)( 59, 60)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 85)( 66, 86)
( 67, 88)( 68, 87)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 73, 93)( 74, 94)
( 75, 96)( 76, 95)( 77, 97)( 78, 98)( 79,100)( 80, 99)(103,104)(107,108)
(111,112)(115,116)(119,120)(121,141)(122,142)(123,144)(124,143)(125,145)
(126,146)(127,148)(128,147)(129,149)(130,150)(131,152)(132,151)(133,153)
(134,154)(135,156)(136,155)(137,157)(138,158)(139,160)(140,159)(163,164)
(167,168)(171,172)(175,176)(179,180)(181,201)(182,202)(183,204)(184,203)
(185,205)(186,206)(187,208)(188,207)(189,209)(190,210)(191,212)(192,211)
(193,213)(194,214)(195,216)(196,215)(197,217)(198,218)(199,220)(200,219)
(223,224)(227,228)(231,232)(235,236)(239,240);
s3 := Sym(240)!(  1,  4)(  5,  8)(  9, 12)( 13, 16)( 17, 20)( 21, 44)( 22, 42)
( 23, 43)( 24, 41)( 25, 48)( 26, 46)( 27, 47)( 28, 45)( 29, 52)( 30, 50)
( 31, 51)( 32, 49)( 33, 56)( 34, 54)( 35, 55)( 36, 53)( 37, 60)( 38, 58)
( 39, 59)( 40, 57)( 61, 64)( 65, 68)( 69, 72)( 73, 76)( 77, 80)( 81,104)
( 82,102)( 83,103)( 84,101)( 85,108)( 86,106)( 87,107)( 88,105)( 89,112)
( 90,110)( 91,111)( 92,109)( 93,116)( 94,114)( 95,115)( 96,113)( 97,120)
( 98,118)( 99,119)(100,117)(121,124)(125,128)(129,132)(133,136)(137,140)
(141,164)(142,162)(143,163)(144,161)(145,168)(146,166)(147,167)(148,165)
(149,172)(150,170)(151,171)(152,169)(153,176)(154,174)(155,175)(156,173)
(157,180)(158,178)(159,179)(160,177)(181,184)(185,188)(189,192)(193,196)
(197,200)(201,224)(202,222)(203,223)(204,221)(205,228)(206,226)(207,227)
(208,225)(209,232)(210,230)(211,231)(212,229)(213,236)(214,234)(215,235)
(216,233)(217,240)(218,238)(219,239)(220,237);
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*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*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