Polytope of Type {2,20,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,24}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150705)
Rank : 4
Schlafli Type : {2,20,24}
Number of vertices, edges, etc : 2, 20, 240, 24
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 : {2,20,12}*960
3-fold quotients : {2,20,8}*640b
4-fold quotients : {2,10,12}*480, {2,20,6}*480a
5-fold quotients : {2,4,24}*384b
6-fold quotients : {2,20,4}*320
8-fold quotients : {2,10,6}*240
10-fold quotients : {2,4,12}*192a
12-fold quotients : {2,20,2}*160, {2,10,4}*160
15-fold quotients : {2,4,8}*128b
20-fold quotients : {2,2,12}*96, {2,4,6}*96a
24-fold quotients : {2,10,2}*80
30-fold quotients : {2,4,4}*64
40-fold quotients : {2,2,6}*48
48-fold quotients : {2,5,2}*40
60-fold quotients : {2,2,4}*32, {2,4,2}*32
80-fold quotients : {2,2,3}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 33, 48)( 34, 52)( 35, 51)( 36, 50)
( 37, 49)( 38, 53)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 58)( 44, 62)
( 45, 61)( 46, 60)( 47, 59)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)
( 75, 76)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 93,108)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,113)( 99,117)(100,116)(101,115)
(102,114)(103,118)(104,122)(105,121)(106,120)(107,119)(123,183)(124,187)
(125,186)(126,185)(127,184)(128,188)(129,192)(130,191)(131,190)(132,189)
(133,193)(134,197)(135,196)(136,195)(137,194)(138,198)(139,202)(140,201)
(141,200)(142,199)(143,203)(144,207)(145,206)(146,205)(147,204)(148,208)
(149,212)(150,211)(151,210)(152,209)(153,228)(154,232)(155,231)(156,230)
(157,229)(158,233)(159,237)(160,236)(161,235)(162,234)(163,238)(164,242)
(165,241)(166,240)(167,239)(168,213)(169,217)(170,216)(171,215)(172,214)
(173,218)(174,222)(175,221)(176,220)(177,219)(178,223)(179,227)(180,226)
(181,225)(182,224);;
s2 := ( 3,124)( 4,123)( 5,127)( 6,126)( 7,125)( 8,134)( 9,133)( 10,137)
( 11,136)( 12,135)( 13,129)( 14,128)( 15,132)( 16,131)( 17,130)( 18,139)
( 19,138)( 20,142)( 21,141)( 22,140)( 23,149)( 24,148)( 25,152)( 26,151)
( 27,150)( 28,144)( 29,143)( 30,147)( 31,146)( 32,145)( 33,169)( 34,168)
( 35,172)( 36,171)( 37,170)( 38,179)( 39,178)( 40,182)( 41,181)( 42,180)
( 43,174)( 44,173)( 45,177)( 46,176)( 47,175)( 48,154)( 49,153)( 50,157)
( 51,156)( 52,155)( 53,164)( 54,163)( 55,167)( 56,166)( 57,165)( 58,159)
( 59,158)( 60,162)( 61,161)( 62,160)( 63,184)( 64,183)( 65,187)( 66,186)
( 67,185)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)( 74,188)
( 75,192)( 76,191)( 77,190)( 78,199)( 79,198)( 80,202)( 81,201)( 82,200)
( 83,209)( 84,208)( 85,212)( 86,211)( 87,210)( 88,204)( 89,203)( 90,207)
( 91,206)( 92,205)( 93,229)( 94,228)( 95,232)( 96,231)( 97,230)( 98,239)
( 99,238)(100,242)(101,241)(102,240)(103,234)(104,233)(105,237)(106,236)
(107,235)(108,214)(109,213)(110,217)(111,216)(112,215)(113,224)(114,223)
(115,227)(116,226)(117,225)(118,219)(119,218)(120,222)(121,221)(122,220);;
s3 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 57)( 38, 48)
( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 43, 58)( 44, 59)( 45, 60)( 46, 61)
( 47, 62)( 63, 83)( 64, 84)( 65, 85)( 66, 86)( 67, 87)( 68, 78)( 69, 79)
( 70, 80)( 71, 81)( 72, 82)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)
( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)
(111,116)(112,117)(123,158)(124,159)(125,160)(126,161)(127,162)(128,153)
(129,154)(130,155)(131,156)(132,157)(133,163)(134,164)(135,165)(136,166)
(137,167)(138,173)(139,174)(140,175)(141,176)(142,177)(143,168)(144,169)
(145,170)(146,171)(147,172)(148,178)(149,179)(150,180)(151,181)(152,182)
(183,233)(184,234)(185,235)(186,236)(187,237)(188,228)(189,229)(190,230)
(191,231)(192,232)(193,238)(194,239)(195,240)(196,241)(197,242)(198,218)
(199,219)(200,220)(201,221)(202,222)(203,213)(204,214)(205,215)(206,216)
(207,217)(208,223)(209,224)(210,225)(211,226)(212,227);;
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,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 33, 48)( 34, 52)( 35, 51)
( 36, 50)( 37, 49)( 38, 53)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 58)
( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 64, 67)( 65, 66)( 69, 72)( 70, 71)
( 74, 77)( 75, 76)( 79, 82)( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)
( 93,108)( 94,112)( 95,111)( 96,110)( 97,109)( 98,113)( 99,117)(100,116)
(101,115)(102,114)(103,118)(104,122)(105,121)(106,120)(107,119)(123,183)
(124,187)(125,186)(126,185)(127,184)(128,188)(129,192)(130,191)(131,190)
(132,189)(133,193)(134,197)(135,196)(136,195)(137,194)(138,198)(139,202)
(140,201)(141,200)(142,199)(143,203)(144,207)(145,206)(146,205)(147,204)
(148,208)(149,212)(150,211)(151,210)(152,209)(153,228)(154,232)(155,231)
(156,230)(157,229)(158,233)(159,237)(160,236)(161,235)(162,234)(163,238)
(164,242)(165,241)(166,240)(167,239)(168,213)(169,217)(170,216)(171,215)
(172,214)(173,218)(174,222)(175,221)(176,220)(177,219)(178,223)(179,227)
(180,226)(181,225)(182,224);
s2 := Sym(242)!( 3,124)( 4,123)( 5,127)( 6,126)( 7,125)( 8,134)( 9,133)
( 10,137)( 11,136)( 12,135)( 13,129)( 14,128)( 15,132)( 16,131)( 17,130)
( 18,139)( 19,138)( 20,142)( 21,141)( 22,140)( 23,149)( 24,148)( 25,152)
( 26,151)( 27,150)( 28,144)( 29,143)( 30,147)( 31,146)( 32,145)( 33,169)
( 34,168)( 35,172)( 36,171)( 37,170)( 38,179)( 39,178)( 40,182)( 41,181)
( 42,180)( 43,174)( 44,173)( 45,177)( 46,176)( 47,175)( 48,154)( 49,153)
( 50,157)( 51,156)( 52,155)( 53,164)( 54,163)( 55,167)( 56,166)( 57,165)
( 58,159)( 59,158)( 60,162)( 61,161)( 62,160)( 63,184)( 64,183)( 65,187)
( 66,186)( 67,185)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)
( 74,188)( 75,192)( 76,191)( 77,190)( 78,199)( 79,198)( 80,202)( 81,201)
( 82,200)( 83,209)( 84,208)( 85,212)( 86,211)( 87,210)( 88,204)( 89,203)
( 90,207)( 91,206)( 92,205)( 93,229)( 94,228)( 95,232)( 96,231)( 97,230)
( 98,239)( 99,238)(100,242)(101,241)(102,240)(103,234)(104,233)(105,237)
(106,236)(107,235)(108,214)(109,213)(110,217)(111,216)(112,215)(113,224)
(114,223)(115,227)(116,226)(117,225)(118,219)(119,218)(120,222)(121,221)
(122,220);
s3 := Sym(242)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 57)
( 38, 48)( 39, 49)( 40, 50)( 41, 51)( 42, 52)( 43, 58)( 44, 59)( 45, 60)
( 46, 61)( 47, 62)( 63, 83)( 64, 84)( 65, 85)( 66, 86)( 67, 87)( 68, 78)
( 69, 79)( 70, 80)( 71, 81)( 72, 82)( 73, 88)( 74, 89)( 75, 90)( 76, 91)
( 77, 92)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)
(110,115)(111,116)(112,117)(123,158)(124,159)(125,160)(126,161)(127,162)
(128,153)(129,154)(130,155)(131,156)(132,157)(133,163)(134,164)(135,165)
(136,166)(137,167)(138,173)(139,174)(140,175)(141,176)(142,177)(143,168)
(144,169)(145,170)(146,171)(147,172)(148,178)(149,179)(150,180)(151,181)
(152,182)(183,233)(184,234)(185,235)(186,236)(187,237)(188,228)(189,229)
(190,230)(191,231)(192,232)(193,238)(194,239)(195,240)(196,241)(197,242)
(198,218)(199,219)(200,220)(201,221)(202,222)(203,213)(204,214)(205,215)
(206,216)(207,217)(208,223)(209,224)(210,225)(211,226)(212,227);
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, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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