Polytope of Type {24,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,20}*960a
Also Known As : {24,20|2}. if this polytope has another name.
Group : SmallGroup(960,2312)
Rank : 3
Schlafli Type : {24,20}
Number of vertices, edges, etc : 24, 240, 20
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 :
{24,20,2} of size 1920
Vertex Figure Of :
{2,24,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,10}*480, {12,20}*480
3-fold quotients : {8,20}*320a
4-fold quotients : {12,10}*240, {6,20}*240a
5-fold quotients : {24,4}*192a
6-fold quotients : {4,20}*160, {8,10}*160
8-fold quotients : {6,10}*120
10-fold quotients : {12,4}*96a, {24,2}*96
12-fold quotients : {2,20}*80, {4,10}*80
15-fold quotients : {8,4}*64a
20-fold quotients : {12,2}*48, {6,4}*48a
24-fold quotients : {2,10}*40
30-fold quotients : {4,4}*32, {8,2}*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}*1920a, {24,40}*1920b, {48,20}*1920a, {48,20}*1920b
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)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)
( 83, 88)( 84, 89)( 85, 90)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)
( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)(103,113)
(104,114)(105,115)(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)
(181,211)(182,212)(183,213)(184,214)(185,215)(186,221)(187,222)(188,223)
(189,224)(190,225)(191,216)(192,217)(193,218)(194,219)(195,220)(196,226)
(197,227)(198,228)(199,229)(200,230)(201,236)(202,237)(203,238)(204,239)
(205,240)(206,231)(207,232)(208,233)(209,234)(210,235);;
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, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 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, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)
(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)(151,212)(152,211)
(153,215)(154,214)(155,213)(156,217)(157,216)(158,220)(159,219)(160,218)
(161,222)(162,221)(163,225)(164,224)(165,223)(166,227)(167,226)(168,230)
(169,229)(170,228)(171,232)(172,231)(173,235)(174,234)(175,233)(176,237)
(177,236)(178,240)(179,239)(180,238);;
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)
( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 91,106)( 92,107)( 93,108)( 94,109)
( 95,110)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)
(103,113)(104,114)(105,115)(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)(181,211)(182,212)(183,213)(184,214)(185,215)(186,221)(187,222)
(188,223)(189,224)(190,225)(191,216)(192,217)(193,218)(194,219)(195,220)
(196,226)(197,227)(198,228)(199,229)(200,230)(201,236)(202,237)(203,238)
(204,239)(205,240)(206,231)(207,232)(208,233)(209,234)(210,235);
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, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 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, 92)( 93, 95)( 96, 97)
( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)
(118,120)(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)(151,212)
(152,211)(153,215)(154,214)(155,213)(156,217)(157,216)(158,220)(159,219)
(160,218)(161,222)(162,221)(163,225)(164,224)(165,223)(166,227)(167,226)
(168,230)(169,229)(170,228)(171,232)(172,231)(173,235)(174,234)(175,233)
(176,237)(177,236)(178,240)(179,239)(180,238);
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope