Polytope of Type {24,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,20}*960b
if this polytope has a name.
Group : SmallGroup(960,2443)
Rank : 3
Schlafli Type : {24,20}
Number of vertices, edges, etc : 24, 240, 20
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 :
{24,20,2} of size 1920
Vertex Figure Of :
{2,24,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,20}*480
3-fold quotients : {8,20}*320b
4-fold quotients : {12,10}*240, {6,20}*240a
5-fold quotients : {24,4}*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 : {8,4}*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 : {24,20}*1920a, {24,40}*1920c, {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)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 56)
( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)( 44, 54)
( 45, 55)( 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)
( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)
(114,119)(115,120)(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)( 31,171)( 32,175)
( 33,174)( 34,173)( 35,172)( 36,166)( 37,170)( 38,169)( 39,168)( 40,167)
( 41,176)( 42,180)( 43,179)( 44,178)( 45,177)( 46,156)( 47,160)( 48,159)
( 49,158)( 50,157)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,161)
( 57,165)( 58,164)( 59,163)( 60,162)( 61,186)( 62,190)( 63,189)( 64,188)
( 65,187)( 66,181)( 67,185)( 68,184)( 69,183)( 70,182)( 71,191)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)
( 81,196)( 82,200)( 83,199)( 84,198)( 85,197)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 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, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)
( 73, 75)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91,107)
( 92,106)( 93,110)( 94,109)( 95,108)( 96,112)( 97,111)( 98,115)( 99,114)
(100,113)(101,117)(102,116)(103,120)(104,119)(105,118)(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,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 56)( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)
( 44, 54)( 45, 55)( 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)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)
(113,118)(114,119)(115,120)(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)( 31,171)
( 32,175)( 33,174)( 34,173)( 35,172)( 36,166)( 37,170)( 38,169)( 39,168)
( 40,167)( 41,176)( 42,180)( 43,179)( 44,178)( 45,177)( 46,156)( 47,160)
( 48,159)( 49,158)( 50,157)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)
( 56,161)( 57,165)( 58,164)( 59,163)( 60,162)( 61,186)( 62,190)( 63,189)
( 64,188)( 65,187)( 66,181)( 67,185)( 68,184)( 69,183)( 70,182)( 71,191)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,201)( 77,205)( 78,204)( 79,203)
( 80,202)( 81,196)( 82,200)( 83,199)( 84,198)( 85,197)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 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, 62)( 63, 65)( 66, 67)( 68, 70)
( 71, 72)( 73, 75)( 76, 77)( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)
( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,112)( 97,111)( 98,115)
( 99,114)(100,113)(101,117)(102,116)(103,120)(104,119)(105,118)(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,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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