Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,20,2}

Atlas Canonical Name {24,20,2}*1920b

Overview

Group
SmallGroup(1920,150705)
Rank
4
Schläfli Type
{24,20,2}
Vertices, edges, …
24, 240, 20, 2
Order of s0s1s2s3
120
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

5-fold

6-fold

8-fold

10-fold

12-fold

15-fold

20-fold

24-fold

30-fold

40-fold

48-fold

60-fold

80-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

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