Polytope of Type {4,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,151306)
Rank : 4
Schlafli Type : {4,12,10}
Number of vertices, edges, etc : 8, 48, 120, 10
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12,10}*960a
   3-fold quotients : {4,4,10}*640
   4-fold quotients : {2,12,10}*480, {4,6,10}*480a
   5-fold quotients : {4,12,2}*384a
   6-fold quotients : {4,4,10}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {4,12,2}*192a
   12-fold quotients : {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {4,4,2}*128
   20-fold quotients : {2,12,2}*96, {4,6,2}*96a
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,4,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope