Polytope of Type {2,24,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148923)
Rank : 4
Schlafli Type : {2,24,20}
Number of vertices, edges, etc : 2, 24, 240, 20
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {2,24,10}*960, {2,12,20}*960
3-fold quotients : {2,8,20}*640a
4-fold quotients : {2,12,10}*480, {2,6,20}*480a
5-fold quotients : {2,24,4}*384a
6-fold quotients : {2,4,20}*320, {2,8,10}*320
8-fold quotients : {2,6,10}*240
10-fold quotients : {2,12,4}*192a, {2,24,2}*192
12-fold quotients : {2,2,20}*160, {2,4,10}*160
15-fold quotients : {2,8,4}*128a
20-fold quotients : {2,12,2}*96, {2,6,4}*96a
24-fold quotients : {2,2,10}*80
30-fold quotients : {2,4,4}*64, {2,8,2}*64
40-fold quotients : {2,6,2}*48
48-fold quotients : {2,2,5}*40
60-fold quotients : {2,2,4}*32, {2,4,2}*32
80-fold quotients : {2,3,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)( 25, 30)
( 26, 31)( 27, 32)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 58)
( 39, 59)( 40, 60)( 41, 61)( 42, 62)( 43, 53)( 44, 54)( 45, 55)( 46, 56)
( 47, 57)( 68, 73)( 69, 74)( 70, 75)( 71, 76)( 72, 77)( 83, 88)( 84, 89)
( 85, 90)( 86, 91)( 87, 92)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)
( 98,118)( 99,119)(100,120)(101,121)(102,122)(103,113)(104,114)(105,115)
(106,116)(107,117)(123,153)(124,154)(125,155)(126,156)(127,157)(128,163)
(129,164)(130,165)(131,166)(132,167)(133,158)(134,159)(135,160)(136,161)
(137,162)(138,168)(139,169)(140,170)(141,171)(142,172)(143,178)(144,179)
(145,180)(146,181)(147,182)(148,173)(149,174)(150,175)(151,176)(152,177)
(183,213)(184,214)(185,215)(186,216)(187,217)(188,223)(189,224)(190,225)
(191,226)(192,227)(193,218)(194,219)(195,220)(196,221)(197,222)(198,228)
(199,229)(200,230)(201,231)(202,232)(203,238)(204,239)(205,240)(206,241)
(207,242)(208,233)(209,234)(210,235)(211,236)(212,237);;
s2 := ( 3,128)( 4,132)( 5,131)( 6,130)( 7,129)( 8,123)( 9,127)( 10,126)
( 11,125)( 12,124)( 13,133)( 14,137)( 15,136)( 16,135)( 17,134)( 18,143)
( 19,147)( 20,146)( 21,145)( 22,144)( 23,138)( 24,142)( 25,141)( 26,140)
( 27,139)( 28,148)( 29,152)( 30,151)( 31,150)( 32,149)( 33,173)( 34,177)
( 35,176)( 36,175)( 37,174)( 38,168)( 39,172)( 40,171)( 41,170)( 42,169)
( 43,178)( 44,182)( 45,181)( 46,180)( 47,179)( 48,158)( 49,162)( 50,161)
( 51,160)( 52,159)( 53,153)( 54,157)( 55,156)( 56,155)( 57,154)( 58,163)
( 59,167)( 60,166)( 61,165)( 62,164)( 63,188)( 64,192)( 65,191)( 66,190)
( 67,189)( 68,183)( 69,187)( 70,186)( 71,185)( 72,184)( 73,193)( 74,197)
( 75,196)( 76,195)( 77,194)( 78,203)( 79,207)( 80,206)( 81,205)( 82,204)
( 83,198)( 84,202)( 85,201)( 86,200)( 87,199)( 88,208)( 89,212)( 90,211)
( 91,210)( 92,209)( 93,233)( 94,237)( 95,236)( 96,235)( 97,234)( 98,228)
( 99,232)(100,231)(101,230)(102,229)(103,238)(104,242)(105,241)(106,240)
(107,239)(108,218)(109,222)(110,221)(111,220)(112,219)(113,213)(114,217)
(115,216)(116,215)(117,214)(118,223)(119,227)(120,226)(121,225)(122,224);;
s3 := ( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)
( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)( 80, 82)
( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)(100,102)
(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)(120,122)
(123,184)(124,183)(125,187)(126,186)(127,185)(128,189)(129,188)(130,192)
(131,191)(132,190)(133,194)(134,193)(135,197)(136,196)(137,195)(138,199)
(139,198)(140,202)(141,201)(142,200)(143,204)(144,203)(145,207)(146,206)
(147,205)(148,209)(149,208)(150,212)(151,211)(152,210)(153,214)(154,213)
(155,217)(156,216)(157,215)(158,219)(159,218)(160,222)(161,221)(162,220)
(163,224)(164,223)(165,227)(166,226)(167,225)(168,229)(169,228)(170,232)
(171,231)(172,230)(173,234)(174,233)(175,237)(176,236)(177,235)(178,239)
(179,238)(180,242)(181,241)(182,240);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(242)!(1,2);
s1 := Sym(242)!( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)
( 38, 58)( 39, 59)( 40, 60)( 41, 61)( 42, 62)( 43, 53)( 44, 54)( 45, 55)
( 46, 56)( 47, 57)( 68, 73)( 69, 74)( 70, 75)( 71, 76)( 72, 77)( 83, 88)
( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 93,108)( 94,109)( 95,110)( 96,111)
( 97,112)( 98,118)( 99,119)(100,120)(101,121)(102,122)(103,113)(104,114)
(105,115)(106,116)(107,117)(123,153)(124,154)(125,155)(126,156)(127,157)
(128,163)(129,164)(130,165)(131,166)(132,167)(133,158)(134,159)(135,160)
(136,161)(137,162)(138,168)(139,169)(140,170)(141,171)(142,172)(143,178)
(144,179)(145,180)(146,181)(147,182)(148,173)(149,174)(150,175)(151,176)
(152,177)(183,213)(184,214)(185,215)(186,216)(187,217)(188,223)(189,224)
(190,225)(191,226)(192,227)(193,218)(194,219)(195,220)(196,221)(197,222)
(198,228)(199,229)(200,230)(201,231)(202,232)(203,238)(204,239)(205,240)
(206,241)(207,242)(208,233)(209,234)(210,235)(211,236)(212,237);
s2 := Sym(242)!( 3,128)( 4,132)( 5,131)( 6,130)( 7,129)( 8,123)( 9,127)
( 10,126)( 11,125)( 12,124)( 13,133)( 14,137)( 15,136)( 16,135)( 17,134)
( 18,143)( 19,147)( 20,146)( 21,145)( 22,144)( 23,138)( 24,142)( 25,141)
( 26,140)( 27,139)( 28,148)( 29,152)( 30,151)( 31,150)( 32,149)( 33,173)
( 34,177)( 35,176)( 36,175)( 37,174)( 38,168)( 39,172)( 40,171)( 41,170)
( 42,169)( 43,178)( 44,182)( 45,181)( 46,180)( 47,179)( 48,158)( 49,162)
( 50,161)( 51,160)( 52,159)( 53,153)( 54,157)( 55,156)( 56,155)( 57,154)
( 58,163)( 59,167)( 60,166)( 61,165)( 62,164)( 63,188)( 64,192)( 65,191)
( 66,190)( 67,189)( 68,183)( 69,187)( 70,186)( 71,185)( 72,184)( 73,193)
( 74,197)( 75,196)( 76,195)( 77,194)( 78,203)( 79,207)( 80,206)( 81,205)
( 82,204)( 83,198)( 84,202)( 85,201)( 86,200)( 87,199)( 88,208)( 89,212)
( 90,211)( 91,210)( 92,209)( 93,233)( 94,237)( 95,236)( 96,235)( 97,234)
( 98,228)( 99,232)(100,231)(101,230)(102,229)(103,238)(104,242)(105,241)
(106,240)(107,239)(108,218)(109,222)(110,221)(111,220)(112,219)(113,213)
(114,217)(115,216)(116,215)(117,214)(118,223)(119,227)(120,226)(121,225)
(122,224);
s3 := Sym(242)!( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)
( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)
(100,102)(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)
(120,122)(123,184)(124,183)(125,187)(126,186)(127,185)(128,189)(129,188)
(130,192)(131,191)(132,190)(133,194)(134,193)(135,197)(136,196)(137,195)
(138,199)(139,198)(140,202)(141,201)(142,200)(143,204)(144,203)(145,207)
(146,206)(147,205)(148,209)(149,208)(150,212)(151,211)(152,210)(153,214)
(154,213)(155,217)(156,216)(157,215)(158,219)(159,218)(160,222)(161,221)
(162,220)(163,224)(164,223)(165,227)(166,226)(167,225)(168,229)(169,228)
(170,232)(171,231)(172,230)(173,234)(174,233)(175,237)(176,236)(177,235)
(178,239)(179,238)(180,242)(181,241)(182,240);
poly := sub<Sym(242)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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 >;
to this polytope