Polytope of Type {2,40,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,40,12}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148921)
Rank : 4
Schlafli Type : {2,40,12}
Number of vertices, edges, etc : 2, 40, 240, 12
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,40,6}*960, {2,20,12}*960
   3-fold quotients : {2,40,4}*640a
   4-fold quotients : {2,10,12}*480, {2,20,6}*480a
   5-fold quotients : {2,8,12}*384a
   6-fold quotients : {2,20,4}*320, {2,40,2}*320
   8-fold quotients : {2,10,6}*240
   10-fold quotients : {2,4,12}*192a, {2,8,6}*192
   12-fold quotients : {2,20,2}*160, {2,10,4}*160
   15-fold quotients : {2,8,4}*128a
   20-fold quotients : {2,2,12}*96, {2,4,6}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,4,4}*64, {2,8,2}*64
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope