Polytope of Type {24,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,20}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42355)
Rank : 3
Schlafli Type : {24,20}
Number of vertices, edges, etc : 48, 480, 40
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 : {12,20}*960a
   3-fold quotients : {8,20}*640b
   4-fold quotients : {12,20}*480
   5-fold quotients : {24,4}*384b
   6-fold quotients : {4,20}*320
   8-fold quotients : {12,10}*240, {6,20}*240a
   10-fold quotients : {12,4}*192a
   12-fold quotients : {4,20}*160
   15-fold quotients : {8,4}*128b
   16-fold quotients : {6,10}*120
   20-fold quotients : {12,4}*96a
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {4,4}*64
   40-fold quotients : {12,2}*48, {6,4}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {6,2}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope