Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,6,20,2}

Atlas Canonical Name {3,6,20,2}*1920

Overview

Group
SmallGroup(1920,240142)
Rank
5
Schläfli Type
{3,6,20,2}
Vertices, edges, …
4, 12, 80, 20, 2
Order of s0s1s2s3s4
20
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

5-fold

10-fold

20-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (  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);;
s1 := (  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);;
s2 := (  1,  4)(  5, 20)(  6, 18)(  7, 19)(  8, 17)(  9, 16)( 10, 14)( 11, 15)( 12, 13)( 21, 44)( 22, 42)( 23, 43)( 24, 41)( 25, 60)( 26, 58)( 27, 59)( 28, 57)( 29, 56)( 30, 54)( 31, 55)( 32, 53)( 33, 52)( 34, 50)( 35, 51)( 36, 49)( 37, 48)( 38, 46)( 39, 47)( 40, 45)( 61, 64)( 65, 80)( 66, 78)( 67, 79)( 68, 77)( 69, 76)( 70, 74)( 71, 75)( 72, 73)( 81,104)( 82,102)( 83,103)( 84,101)( 85,120)( 86,118)( 87,119)( 88,117)( 89,116)( 90,114)( 91,115)( 92,113)( 93,112)( 94,110)( 95,111)( 96,109)( 97,108)( 98,106)( 99,107)(100,105)(121,184)(122,182)(123,183)(124,181)(125,200)(126,198)(127,199)(128,197)(129,196)(130,194)(131,195)(132,193)(133,192)(134,190)(135,191)(136,189)(137,188)(138,186)(139,187)(140,185)(141,224)(142,222)(143,223)(144,221)(145,240)(146,238)(147,239)(148,237)(149,236)(150,234)(151,235)(152,233)(153,232)(154,230)(155,231)(156,229)(157,228)(158,226)(159,227)(160,225)(161,204)(162,202)(163,203)(164,201)(165,220)(166,218)(167,219)(168,217)(169,216)(170,214)(171,215)(172,213)(173,212)(174,210)(175,211)(176,209)(177,208)(178,206)(179,207)(180,205);;
s3 := (  1,125)(  2,126)(  3,127)(  4,128)(  5,121)(  6,122)(  7,123)(  8,124)(  9,137)( 10,138)( 11,139)( 12,140)( 13,133)( 14,134)( 15,135)( 16,136)( 17,129)( 18,130)( 19,131)( 20,132)( 21,145)( 22,146)( 23,147)( 24,148)( 25,141)( 26,142)( 27,143)( 28,144)( 29,157)( 30,158)( 31,159)( 32,160)( 33,153)( 34,154)( 35,155)( 36,156)( 37,149)( 38,150)( 39,151)( 40,152)( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)( 48,164)( 49,177)( 50,178)( 51,179)( 52,180)( 53,173)( 54,174)( 55,175)( 56,176)( 57,169)( 58,170)( 59,171)( 60,172)( 61,185)( 62,186)( 63,187)( 64,188)( 65,181)( 66,182)( 67,183)( 68,184)( 69,197)( 70,198)( 71,199)( 72,200)( 73,193)( 74,194)( 75,195)( 76,196)( 77,189)( 78,190)( 79,191)( 80,192)( 81,205)( 82,206)( 83,207)( 84,208)( 85,201)( 86,202)( 87,203)( 88,204)( 89,217)( 90,218)( 91,219)( 92,220)( 93,213)( 94,214)( 95,215)( 96,216)( 97,209)( 98,210)( 99,211)(100,212)(101,225)(102,226)(103,227)(104,228)(105,221)(106,222)(107,223)(108,224)(109,237)(110,238)(111,239)(112,240)(113,233)(114,234)(115,235)(116,236)(117,229)(118,230)(119,231)(120,232);;
s4 := (241,242);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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)!(  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);
s1 := Sym(242)!(  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);
s2 := Sym(242)!(  1,  4)(  5, 20)(  6, 18)(  7, 19)(  8, 17)(  9, 16)( 10, 14)( 11, 15)( 12, 13)( 21, 44)( 22, 42)( 23, 43)( 24, 41)( 25, 60)( 26, 58)( 27, 59)( 28, 57)( 29, 56)( 30, 54)( 31, 55)( 32, 53)( 33, 52)( 34, 50)( 35, 51)( 36, 49)( 37, 48)( 38, 46)( 39, 47)( 40, 45)( 61, 64)( 65, 80)( 66, 78)( 67, 79)( 68, 77)( 69, 76)( 70, 74)( 71, 75)( 72, 73)( 81,104)( 82,102)( 83,103)( 84,101)( 85,120)( 86,118)( 87,119)( 88,117)( 89,116)( 90,114)( 91,115)( 92,113)( 93,112)( 94,110)( 95,111)( 96,109)( 97,108)( 98,106)( 99,107)(100,105)(121,184)(122,182)(123,183)(124,181)(125,200)(126,198)(127,199)(128,197)(129,196)(130,194)(131,195)(132,193)(133,192)(134,190)(135,191)(136,189)(137,188)(138,186)(139,187)(140,185)(141,224)(142,222)(143,223)(144,221)(145,240)(146,238)(147,239)(148,237)(149,236)(150,234)(151,235)(152,233)(153,232)(154,230)(155,231)(156,229)(157,228)(158,226)(159,227)(160,225)(161,204)(162,202)(163,203)(164,201)(165,220)(166,218)(167,219)(168,217)(169,216)(170,214)(171,215)(172,213)(173,212)(174,210)(175,211)(176,209)(177,208)(178,206)(179,207)(180,205);
s3 := Sym(242)!(  1,125)(  2,126)(  3,127)(  4,128)(  5,121)(  6,122)(  7,123)(  8,124)(  9,137)( 10,138)( 11,139)( 12,140)( 13,133)( 14,134)( 15,135)( 16,136)( 17,129)( 18,130)( 19,131)( 20,132)( 21,145)( 22,146)( 23,147)( 24,148)( 25,141)( 26,142)( 27,143)( 28,144)( 29,157)( 30,158)( 31,159)( 32,160)( 33,153)( 34,154)( 35,155)( 36,156)( 37,149)( 38,150)( 39,151)( 40,152)( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)( 48,164)( 49,177)( 50,178)( 51,179)( 52,180)( 53,173)( 54,174)( 55,175)( 56,176)( 57,169)( 58,170)( 59,171)( 60,172)( 61,185)( 62,186)( 63,187)( 64,188)( 65,181)( 66,182)( 67,183)( 68,184)( 69,197)( 70,198)( 71,199)( 72,200)( 73,193)( 74,194)( 75,195)( 76,196)( 77,189)( 78,190)( 79,191)( 80,192)( 81,205)( 82,206)( 83,207)( 84,208)( 85,201)( 86,202)( 87,203)( 88,204)( 89,217)( 90,218)( 91,219)( 92,220)( 93,213)( 94,214)( 95,215)( 96,216)( 97,209)( 98,210)( 99,211)(100,212)(101,225)(102,226)(103,227)(104,228)(105,221)(106,222)(107,223)(108,224)(109,237)(110,238)(111,239)(112,240)(113,233)(114,234)(115,235)(116,236)(117,229)(118,230)(119,231)(120,232);
s4 := Sym(242)!(241,242);
poly := sub<Sym(242)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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 >;