Polytope of Type {40,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,12}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42353)
Rank : 3
Schlafli Type : {40,12}
Number of vertices, edges, etc : 80, 480, 24
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {20,12}*960a
   3-fold quotients : {40,4}*640b
   4-fold quotients : {20,12}*480
   5-fold quotients : {8,12}*384b
   6-fold quotients : {20,4}*320
   8-fold quotients : {10,12}*240, {20,6}*240a
   10-fold quotients : {4,12}*192a
   12-fold quotients : {20,4}*160
   15-fold quotients : {8,4}*128b
   16-fold quotients : {10,6}*120
   20-fold quotients : {4,12}*96a
   24-fold quotients : {20,2}*80, {10,4}*80
   30-fold quotients : {4,4}*64
   40-fold quotients : {2,12}*48, {4,6}*48a
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope