Part of the Atlas of Small Regular Polytopes

Polytope of Type {240,2,2}

Atlas Canonical Name {240,2,2}*1920

Overview

Group
SmallGroup(1920,203900)
Rank
4
Schläfli Type
{240,2,2}
Vertices, edges, …
240, 240, 2, 2
Order of s0s1s2s3
240
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

16-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 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66,101)( 67,105)( 68,104)( 69,103)( 70,102)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,116)( 82,120)( 83,119)( 84,118)( 85,117)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)(175,222)(176,216)(177,220)(178,219)(179,218)(180,217);;
s1 := (  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,172)( 32,171)( 33,175)( 34,174)( 35,173)( 36,167)( 37,166)( 38,170)( 39,169)( 40,168)( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,157)( 47,156)( 48,160)( 49,159)( 50,158)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,217)( 62,216)( 63,220)( 64,219)( 65,218)( 66,212)( 67,211)( 68,215)( 69,214)( 70,213)( 71,222)( 72,221)( 73,225)( 74,224)( 75,223)( 76,232)( 77,231)( 78,235)( 79,234)( 80,233)( 81,227)( 82,226)( 83,230)( 84,229)( 85,228)( 86,237)( 87,236)( 88,240)( 89,239)( 90,238)( 91,187)( 92,186)( 93,190)( 94,189)( 95,188)( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,192)(102,191)(103,195)(104,194)(105,193)(106,202)(107,201)(108,205)(109,204)(110,203)(111,197)(112,196)(113,200)(114,199)(115,198)(116,207)(117,206)(118,210)(119,209)(120,208);;
s2 := (241,242);;
s3 := (243,244);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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*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*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*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*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*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*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*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*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*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*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(244)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)( 66,101)( 67,105)( 68,104)( 69,103)( 70,102)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,116)( 82,120)( 83,119)( 84,118)( 85,117)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112)(121,181)(122,185)(123,184)(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)(149,203)(150,202)(151,226)(152,230)(153,229)(154,228)(155,227)(156,236)(157,240)(158,239)(159,238)(160,237)(161,231)(162,235)(163,234)(164,233)(165,232)(166,211)(167,215)(168,214)(169,213)(170,212)(171,221)(172,225)(173,224)(174,223)(175,222)(176,216)(177,220)(178,219)(179,218)(180,217);
s1 := Sym(244)!(  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,172)( 32,171)( 33,175)( 34,174)( 35,173)( 36,167)( 37,166)( 38,170)( 39,169)( 40,168)( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,157)( 47,156)( 48,160)( 49,159)( 50,158)( 51,152)( 52,151)( 53,155)( 54,154)( 55,153)( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,217)( 62,216)( 63,220)( 64,219)( 65,218)( 66,212)( 67,211)( 68,215)( 69,214)( 70,213)( 71,222)( 72,221)( 73,225)( 74,224)( 75,223)( 76,232)( 77,231)( 78,235)( 79,234)( 80,233)( 81,227)( 82,226)( 83,230)( 84,229)( 85,228)( 86,237)( 87,236)( 88,240)( 89,239)( 90,238)( 91,187)( 92,186)( 93,190)( 94,189)( 95,188)( 96,182)( 97,181)( 98,185)( 99,184)(100,183)(101,192)(102,191)(103,195)(104,194)(105,193)(106,202)(107,201)(108,205)(109,204)(110,203)(111,197)(112,196)(113,200)(114,199)(115,198)(116,207)(117,206)(118,210)(119,209)(120,208);
s2 := Sym(244)!(241,242);
s3 := Sym(244)!(243,244);
poly := sub<Sym(244)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*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*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*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*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*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*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*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*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*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*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*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 >;