Polytope of Type {10,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,151306)
Rank : 4
Schlafli Type : {10,12,4}
Number of vertices, edges, etc : 10, 120, 48, 8
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 : {10,12,4}*960a
   3-fold quotients : {10,4,4}*640
   4-fold quotients : {10,12,2}*480, {10,6,4}*480a
   5-fold quotients : {2,12,4}*384a
   6-fold quotients : {10,4,4}*320
   8-fold quotients : {10,6,2}*240
   10-fold quotients : {2,12,4}*192a
   12-fold quotients : {10,2,4}*160, {10,4,2}*160
   15-fold quotients : {2,4,4}*128
   20-fold quotients : {2,12,2}*96, {2,6,4}*96a
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   30-fold quotients : {2,4,4}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*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 := (  1, 61)(  2, 65)(  3, 64)(  4, 63)(  5, 62)(  6, 66)(  7, 70)(  8, 69)
(  9, 68)( 10, 67)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 76)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 81)( 22, 85)( 23, 84)( 24, 83)
( 25, 82)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 91)( 32, 95)
( 33, 94)( 34, 93)( 35, 92)( 36, 96)( 37,100)( 38, 99)( 39, 98)( 40, 97)
( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,106)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,111)( 52,115)( 53,114)( 54,113)( 55,112)( 56,116)
( 57,120)( 58,119)( 59,118)( 60,117)(121,181)(122,185)(123,184)(124,183)
(125,182)(126,186)(127,190)(128,189)(129,188)(130,187)(131,191)(132,195)
(133,194)(134,193)(135,192)(136,196)(137,200)(138,199)(139,198)(140,197)
(141,201)(142,205)(143,204)(144,203)(145,202)(146,206)(147,210)(148,209)
(149,208)(150,207)(151,211)(152,215)(153,214)(154,213)(155,212)(156,216)
(157,220)(158,219)(159,218)(160,217)(161,221)(162,225)(163,224)(164,223)
(165,222)(166,226)(167,230)(168,229)(169,228)(170,227)(171,231)(172,235)
(173,234)(174,233)(175,232)(176,236)(177,240)(178,239)(179,238)(180,237);;
s1 := (  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,192)(  7,191)(  8,195)
(  9,194)( 10,193)( 11,187)( 12,186)( 13,190)( 14,189)( 15,188)( 16,197)
( 17,196)( 18,200)( 19,199)( 20,198)( 21,207)( 22,206)( 23,210)( 24,209)
( 25,208)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,212)( 32,211)
( 33,215)( 34,214)( 35,213)( 36,222)( 37,221)( 38,225)( 39,224)( 40,223)
( 41,217)( 42,216)( 43,220)( 44,219)( 45,218)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)( 56,232)
( 57,231)( 58,235)( 59,234)( 60,233)( 61,122)( 62,121)( 63,125)( 64,124)
( 65,123)( 66,132)( 67,131)( 68,135)( 69,134)( 70,133)( 71,127)( 72,126)
( 73,130)( 74,129)( 75,128)( 76,137)( 77,136)( 78,140)( 79,139)( 80,138)
( 81,147)( 82,146)( 83,150)( 84,149)( 85,148)( 86,142)( 87,141)( 88,145)
( 89,144)( 90,143)( 91,152)( 92,151)( 93,155)( 94,154)( 95,153)( 96,162)
( 97,161)( 98,165)( 99,164)(100,163)(101,157)(102,156)(103,160)(104,159)
(105,158)(106,167)(107,166)(108,170)(109,169)(110,168)(111,177)(112,176)
(113,180)(114,179)(115,178)(116,172)(117,171)(118,175)(119,174)(120,173);;
s2 := (  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)
( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)( 64, 69)
( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)( 92, 97)
( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)(110,115)
(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)
(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165)(136,171)
(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)(143,168)(144,169)
(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)(181,216)(182,217)
(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)(189,214)(190,215)
(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)(197,232)(198,233)
(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)(205,230)(206,236)
(207,237)(208,238)(209,239)(210,240);;
s3 := ( 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);;
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*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(  1, 61)(  2, 65)(  3, 64)(  4, 63)(  5, 62)(  6, 66)(  7, 70)
(  8, 69)(  9, 68)( 10, 67)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 81)( 22, 85)( 23, 84)
( 24, 83)( 25, 82)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 91)
( 32, 95)( 33, 94)( 34, 93)( 35, 92)( 36, 96)( 37,100)( 38, 99)( 39, 98)
( 40, 97)( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,106)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,111)( 52,115)( 53,114)( 54,113)( 55,112)
( 56,116)( 57,120)( 58,119)( 59,118)( 60,117)(121,181)(122,185)(123,184)
(124,183)(125,182)(126,186)(127,190)(128,189)(129,188)(130,187)(131,191)
(132,195)(133,194)(134,193)(135,192)(136,196)(137,200)(138,199)(139,198)
(140,197)(141,201)(142,205)(143,204)(144,203)(145,202)(146,206)(147,210)
(148,209)(149,208)(150,207)(151,211)(152,215)(153,214)(154,213)(155,212)
(156,216)(157,220)(158,219)(159,218)(160,217)(161,221)(162,225)(163,224)
(164,223)(165,222)(166,226)(167,230)(168,229)(169,228)(170,227)(171,231)
(172,235)(173,234)(174,233)(175,232)(176,236)(177,240)(178,239)(179,238)
(180,237);
s1 := Sym(240)!(  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,192)(  7,191)
(  8,195)(  9,194)( 10,193)( 11,187)( 12,186)( 13,190)( 14,189)( 15,188)
( 16,197)( 17,196)( 18,200)( 19,199)( 20,198)( 21,207)( 22,206)( 23,210)
( 24,209)( 25,208)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,212)
( 32,211)( 33,215)( 34,214)( 35,213)( 36,222)( 37,221)( 38,225)( 39,224)
( 40,223)( 41,217)( 42,216)( 43,220)( 44,219)( 45,218)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)
( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,122)( 62,121)( 63,125)
( 64,124)( 65,123)( 66,132)( 67,131)( 68,135)( 69,134)( 70,133)( 71,127)
( 72,126)( 73,130)( 74,129)( 75,128)( 76,137)( 77,136)( 78,140)( 79,139)
( 80,138)( 81,147)( 82,146)( 83,150)( 84,149)( 85,148)( 86,142)( 87,141)
( 88,145)( 89,144)( 90,143)( 91,152)( 92,151)( 93,155)( 94,154)( 95,153)
( 96,162)( 97,161)( 98,165)( 99,164)(100,163)(101,157)(102,156)(103,160)
(104,159)(105,158)(106,167)(107,166)(108,170)(109,169)(110,168)(111,177)
(112,176)(113,180)(114,179)(115,178)(116,172)(117,171)(118,175)(119,174)
(120,173);
s2 := Sym(240)!(  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)
( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)
( 64, 69)( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)
( 92, 97)( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)
(110,115)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)
(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165)
(136,171)(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)(143,168)
(144,169)(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)(181,216)
(182,217)(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)(189,214)
(190,215)(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)(197,232)
(198,233)(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)(205,230)
(206,236)(207,237)(208,238)(209,239)(210,240);
s3 := 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);
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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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