Polytope of Type {12,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,40}*960b
if this polytope has a name.
Group : SmallGroup(960,2444)
Rank : 3
Schlafli Type : {12,40}
Number of vertices, edges, etc : 12, 240, 40
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,40,2} of size 1920
Vertex Figure Of :
   {2,12,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,20}*480
   3-fold quotients : {4,40}*320b
   4-fold quotients : {12,10}*240, {6,20}*240a
   5-fold quotients : {12,8}*192b
   6-fold quotients : {4,20}*160
   8-fold quotients : {6,10}*120
   10-fold quotients : {12,4}*96a
   12-fold quotients : {2,20}*80, {4,10}*80
   15-fold quotients : {4,8}*64b
   20-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {2,10}*40
   30-fold quotients : {4,4}*32
   40-fold quotients : {6,2}*24
   48-fold quotients : {2,5}*20
   60-fold quotients : {2,4}*16, {4,2}*16
   80-fold quotients : {3,2}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,40}*1920a, {24,40}*1920b, {24,40}*1920d
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*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*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*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*s0*s1*s2*s1 >;

References : None.
to this polytope