Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12,10}

Atlas Canonical Name {4,12,10}*1920c

Overview

Group
SmallGroup(1920,240151)
Rank
4
Schläfli Type
{4,12,10}
Vertices, edges, …
8, 48, 120, 10
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

8-fold

10-fold

20-fold

24-fold

40-fold

48-fold

80-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2

10 facets

4 vertex figures

P/N, where N=<(s0*s1)^2> of order 2

10 facets

4 vertex figures

Representations

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

References

None.

to this polytope.