Polytope of Type {20,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12}*1920a
if this polytope has a name.
Group : SmallGroup(1920,42362)
Rank : 3
Schlafli Type : {20,12}
Number of vertices, edges, etc : 80, 480, 48
Order of s₀s₁s₂ : 120
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 : {20,4}*640a
   4-fold quotients : {20,12}*480
   5-fold quotients : {4,12}*384a
   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 : {4,4}*128
   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)( 61,181)( 62,185)( 63,184)( 64,183)
( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,216)
( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)(104,223)
(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)(112,235)
(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)(120,237);;
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,  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)( 61,111)( 62,112)( 63,113)( 64,114)
( 65,115)( 66,106)( 67,107)( 68,108)( 69,109)( 70,110)( 71,116)( 72,117)
( 73,118)( 74,119)( 75,120)( 76, 96)( 77, 97)( 78, 98)( 79, 99)( 80,100)
( 81, 91)( 82, 92)( 83, 93)( 84, 94)( 85, 95)( 86,101)( 87,102)( 88,103)
( 89,104)( 90,105)(121,126)(122,127)(123,128)(124,129)(125,130)(136,141)
(137,142)(138,143)(139,144)(140,145)(151,156)(152,157)(153,158)(154,159)
(155,160)(166,171)(167,172)(168,173)(169,174)(170,175)(181,231)(182,232)
(183,233)(184,234)(185,235)(186,226)(187,227)(188,228)(189,229)(190,230)
(191,236)(192,237)(193,238)(194,239)(195,240)(196,216)(197,217)(198,218)
(199,219)(200,220)(201,211)(202,212)(203,213)(204,214)(205,215)(206,221)
(207,222)(208,223)(209,224)(210,225);;
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, 
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*s0*s1*s0*s1*s0*s1*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)( 61,181)( 62,185)( 63,184)
( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,216)( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)
(104,223)(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)
(112,235)(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)
(120,237);
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,  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)( 61,111)( 62,112)( 63,113)
( 64,114)( 65,115)( 66,106)( 67,107)( 68,108)( 69,109)( 70,110)( 71,116)
( 72,117)( 73,118)( 74,119)( 75,120)( 76, 96)( 77, 97)( 78, 98)( 79, 99)
( 80,100)( 81, 91)( 82, 92)( 83, 93)( 84, 94)( 85, 95)( 86,101)( 87,102)
( 88,103)( 89,104)( 90,105)(121,126)(122,127)(123,128)(124,129)(125,130)
(136,141)(137,142)(138,143)(139,144)(140,145)(151,156)(152,157)(153,158)
(154,159)(155,160)(166,171)(167,172)(168,173)(169,174)(170,175)(181,231)
(182,232)(183,233)(184,234)(185,235)(186,226)(187,227)(188,228)(189,229)
(190,230)(191,236)(192,237)(193,238)(194,239)(195,240)(196,216)(197,217)
(198,218)(199,219)(200,220)(201,211)(202,212)(203,213)(204,214)(205,215)
(206,221)(207,222)(208,223)(209,224)(210,225);
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, 
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope