Polytope of Type {20,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,24}*960a
Also Known As : {20,24|2}. if this polytope has another name.
Group : SmallGroup(960,2312)
Rank : 3
Schlafli Type : {20,24}
Number of vertices, edges, etc : 20, 240, 24
Order of s0s1s2 : 120
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,24,2} of size 1920
Vertex Figure Of :
{2,20,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,24}*480, {20,12}*480
3-fold quotients : {20,8}*320a
4-fold quotients : {10,12}*240, {20,6}*240a
5-fold quotients : {4,24}*192a
6-fold quotients : {20,4}*160, {10,8}*160
8-fold quotients : {10,6}*120
10-fold quotients : {4,12}*96a, {2,24}*96
12-fold quotients : {20,2}*80, {10,4}*80
15-fold quotients : {4,8}*64a
20-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {10,2}*40
30-fold quotients : {4,4}*32, {2,8}*32
40-fold quotients : {2,6}*24
48-fold quotients : {5,2}*20
60-fold quotients : {2,4}*16, {4,2}*16
80-fold quotients : {2,3}*12
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,24}*1920a, {40,24}*1920a, {40,24}*1920b, {20,48}*1920a, {20,48}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(121,181)(122,185)(123,184)(124,183)(125,182)(126,186)(127,190)(128,189)
(129,188)(130,187)(131,191)(132,195)(133,194)(134,193)(135,192)(136,196)
(137,200)(138,199)(139,198)(140,197)(141,201)(142,205)(143,204)(144,203)
(145,202)(146,206)(147,210)(148,209)(149,208)(150,207)(151,211)(152,215)
(153,214)(154,213)(155,212)(156,216)(157,220)(158,219)(159,218)(160,217)
(161,221)(162,225)(163,224)(164,223)(165,222)(166,226)(167,230)(168,229)
(169,228)(170,227)(171,231)(172,235)(173,234)(174,233)(175,232)(176,236)
(177,240)(178,239)(179,238)(180,237);;
s1 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,132)( 7,131)( 8,135)
( 9,134)( 10,133)( 11,127)( 12,126)( 13,130)( 14,129)( 15,128)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)( 24,149)
( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,167)( 32,166)
( 33,170)( 34,169)( 35,168)( 36,177)( 37,176)( 38,180)( 39,179)( 40,178)
( 41,172)( 42,171)( 43,175)( 44,174)( 45,173)( 46,152)( 47,151)( 48,155)
( 49,154)( 50,153)( 51,162)( 52,161)( 53,165)( 54,164)( 55,163)( 56,157)
( 57,156)( 58,160)( 59,159)( 60,158)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,192)( 67,191)( 68,195)( 69,194)( 70,193)( 71,187)( 72,186)
( 73,190)( 74,189)( 75,188)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,202)( 87,201)( 88,205)
( 89,204)( 90,203)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)( 96,237)
( 97,236)( 98,240)( 99,239)(100,238)(101,232)(102,231)(103,235)(104,234)
(105,233)(106,212)(107,211)(108,215)(109,214)(110,213)(111,222)(112,221)
(113,225)(114,224)(115,223)(116,217)(117,216)(118,220)(119,219)(120,218);;
s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 51)( 32, 52)( 33, 53)( 34, 54)( 35, 55)( 36, 46)
( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 41, 56)( 42, 57)( 43, 58)( 44, 59)
( 45, 60)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 76, 81)( 77, 82)
( 78, 83)( 79, 84)( 80, 85)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)
( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)
(104,119)(105,120)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)
(127,152)(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)
(135,165)(136,171)(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)
(143,168)(144,169)(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)
(181,216)(182,217)(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)
(189,214)(190,215)(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)
(197,232)(198,233)(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)
(205,230)(206,236)(207,237)(208,238)(209,239)(210,240);;
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(121,181)(122,185)(123,184)(124,183)(125,182)(126,186)(127,190)
(128,189)(129,188)(130,187)(131,191)(132,195)(133,194)(134,193)(135,192)
(136,196)(137,200)(138,199)(139,198)(140,197)(141,201)(142,205)(143,204)
(144,203)(145,202)(146,206)(147,210)(148,209)(149,208)(150,207)(151,211)
(152,215)(153,214)(154,213)(155,212)(156,216)(157,220)(158,219)(159,218)
(160,217)(161,221)(162,225)(163,224)(164,223)(165,222)(166,226)(167,230)
(168,229)(169,228)(170,227)(171,231)(172,235)(173,234)(174,233)(175,232)
(176,236)(177,240)(178,239)(179,238)(180,237);
s1 := Sym(240)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,132)( 7,131)
( 8,135)( 9,134)( 10,133)( 11,127)( 12,126)( 13,130)( 14,129)( 15,128)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)
( 24,149)( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,167)
( 32,166)( 33,170)( 34,169)( 35,168)( 36,177)( 37,176)( 38,180)( 39,179)
( 40,178)( 41,172)( 42,171)( 43,175)( 44,174)( 45,173)( 46,152)( 47,151)
( 48,155)( 49,154)( 50,153)( 51,162)( 52,161)( 53,165)( 54,164)( 55,163)
( 56,157)( 57,156)( 58,160)( 59,159)( 60,158)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,192)( 67,191)( 68,195)( 69,194)( 70,193)( 71,187)
( 72,186)( 73,190)( 74,189)( 75,188)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,202)( 87,201)
( 88,205)( 89,204)( 90,203)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)
( 96,237)( 97,236)( 98,240)( 99,239)(100,238)(101,232)(102,231)(103,235)
(104,234)(105,233)(106,212)(107,211)(108,215)(109,214)(110,213)(111,222)
(112,221)(113,225)(114,224)(115,223)(116,217)(117,216)(118,220)(119,219)
(120,218);
s2 := Sym(240)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 51)( 32, 52)( 33, 53)( 34, 54)( 35, 55)
( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 41, 56)( 42, 57)( 43, 58)
( 44, 59)( 45, 60)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 76, 81)
( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91,111)( 92,112)( 93,113)( 94,114)
( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)
(103,118)(104,119)(105,120)(121,156)(122,157)(123,158)(124,159)(125,160)
(126,151)(127,152)(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)
(134,164)(135,165)(136,171)(137,172)(138,173)(139,174)(140,175)(141,166)
(142,167)(143,168)(144,169)(145,170)(146,176)(147,177)(148,178)(149,179)
(150,180)(181,216)(182,217)(183,218)(184,219)(185,220)(186,211)(187,212)
(188,213)(189,214)(190,215)(191,221)(192,222)(193,223)(194,224)(195,225)
(196,231)(197,232)(198,233)(199,234)(200,235)(201,226)(202,227)(203,228)
(204,229)(205,230)(206,236)(207,237)(208,238)(209,239)(210,240);
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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