Polytope of Type {2,12,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,20}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 4
Schlafli Type : {2,12,20}
Number of vertices, edges, etc : 2, 24, 240, 40
Order of s0s1s2s3 : 60
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 : {2,6,20}*960c
4-fold quotients : {2,12,10}*480, {2,6,20}*480b
5-fold quotients : {2,12,4}*384b
8-fold quotients : {2,6,10}*240
10-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
12-fold quotients : {2,4,10}*160
20-fold quotients : {2,12,2}*96, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
24-fold quotients : {2,2,10}*80
40-fold quotients : {2,3,4}*48, {2,6,2}*48
48-fold quotients : {2,2,5}*40
60-fold quotients : {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 := ( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)( 25, 44)
( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)( 33, 52)
( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)( 41, 60)
( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)( 92,113)
( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)(100,121)
(101,120)(102,122)(123,183)(124,185)(125,184)(126,186)(127,187)(128,189)
(129,188)(130,190)(131,191)(132,193)(133,192)(134,194)(135,195)(136,197)
(137,196)(138,198)(139,199)(140,201)(141,200)(142,202)(143,223)(144,225)
(145,224)(146,226)(147,227)(148,229)(149,228)(150,230)(151,231)(152,233)
(153,232)(154,234)(155,235)(156,237)(157,236)(158,238)(159,239)(160,241)
(161,240)(162,242)(163,203)(164,205)(165,204)(166,206)(167,207)(168,209)
(169,208)(170,210)(171,211)(172,213)(173,212)(174,214)(175,215)(176,217)
(177,216)(178,218)(179,219)(180,221)(181,220)(182,222);;
s2 := ( 3,143)( 4,144)( 5,146)( 6,145)( 7,159)( 8,160)( 9,162)( 10,161)
( 11,155)( 12,156)( 13,158)( 14,157)( 15,151)( 16,152)( 17,154)( 18,153)
( 19,147)( 20,148)( 21,150)( 22,149)( 23,123)( 24,124)( 25,126)( 26,125)
( 27,139)( 28,140)( 29,142)( 30,141)( 31,135)( 32,136)( 33,138)( 34,137)
( 35,131)( 36,132)( 37,134)( 38,133)( 39,127)( 40,128)( 41,130)( 42,129)
( 43,163)( 44,164)( 45,166)( 46,165)( 47,179)( 48,180)( 49,182)( 50,181)
( 51,175)( 52,176)( 53,178)( 54,177)( 55,171)( 56,172)( 57,174)( 58,173)
( 59,167)( 60,168)( 61,170)( 62,169)( 63,203)( 64,204)( 65,206)( 66,205)
( 67,219)( 68,220)( 69,222)( 70,221)( 71,215)( 72,216)( 73,218)( 74,217)
( 75,211)( 76,212)( 77,214)( 78,213)( 79,207)( 80,208)( 81,210)( 82,209)
( 83,183)( 84,184)( 85,186)( 86,185)( 87,199)( 88,200)( 89,202)( 90,201)
( 91,195)( 92,196)( 93,198)( 94,197)( 95,191)( 96,192)( 97,194)( 98,193)
( 99,187)(100,188)(101,190)(102,189)(103,223)(104,224)(105,226)(106,225)
(107,239)(108,240)(109,242)(110,241)(111,235)(112,236)(113,238)(114,237)
(115,231)(116,232)(117,234)(118,233)(119,227)(120,228)(121,230)(122,229);;
s3 := ( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 11, 22)( 12, 21)( 13, 20)( 14, 19)
( 15, 18)( 16, 17)( 23, 30)( 24, 29)( 25, 28)( 26, 27)( 31, 42)( 32, 41)
( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 63, 70)( 64, 69)
( 65, 68)( 66, 67)( 71, 82)( 72, 81)( 73, 80)( 74, 79)( 75, 78)( 76, 77)
( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 91,102)( 92,101)( 93,100)( 94, 99)
( 95, 98)( 96, 97)(103,110)(104,109)(105,108)(106,107)(111,122)(112,121)
(113,120)(114,119)(115,118)(116,117)(123,130)(124,129)(125,128)(126,127)
(131,142)(132,141)(133,140)(134,139)(135,138)(136,137)(143,150)(144,149)
(145,148)(146,147)(151,162)(152,161)(153,160)(154,159)(155,158)(156,157)
(163,170)(164,169)(165,168)(166,167)(171,182)(172,181)(173,180)(174,179)
(175,178)(176,177)(183,190)(184,189)(185,188)(186,187)(191,202)(192,201)
(193,200)(194,199)(195,198)(196,197)(203,210)(204,209)(205,208)(206,207)
(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,230)(224,229)
(225,228)(226,227)(231,242)(232,241)(233,240)(234,239)(235,238)(236,237);;
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*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)
( 25, 44)( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)
( 33, 52)( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)
( 41, 60)( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)
( 92,113)( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)
(100,121)(101,120)(102,122)(123,183)(124,185)(125,184)(126,186)(127,187)
(128,189)(129,188)(130,190)(131,191)(132,193)(133,192)(134,194)(135,195)
(136,197)(137,196)(138,198)(139,199)(140,201)(141,200)(142,202)(143,223)
(144,225)(145,224)(146,226)(147,227)(148,229)(149,228)(150,230)(151,231)
(152,233)(153,232)(154,234)(155,235)(156,237)(157,236)(158,238)(159,239)
(160,241)(161,240)(162,242)(163,203)(164,205)(165,204)(166,206)(167,207)
(168,209)(169,208)(170,210)(171,211)(172,213)(173,212)(174,214)(175,215)
(176,217)(177,216)(178,218)(179,219)(180,221)(181,220)(182,222);
s2 := Sym(242)!( 3,143)( 4,144)( 5,146)( 6,145)( 7,159)( 8,160)( 9,162)
( 10,161)( 11,155)( 12,156)( 13,158)( 14,157)( 15,151)( 16,152)( 17,154)
( 18,153)( 19,147)( 20,148)( 21,150)( 22,149)( 23,123)( 24,124)( 25,126)
( 26,125)( 27,139)( 28,140)( 29,142)( 30,141)( 31,135)( 32,136)( 33,138)
( 34,137)( 35,131)( 36,132)( 37,134)( 38,133)( 39,127)( 40,128)( 41,130)
( 42,129)( 43,163)( 44,164)( 45,166)( 46,165)( 47,179)( 48,180)( 49,182)
( 50,181)( 51,175)( 52,176)( 53,178)( 54,177)( 55,171)( 56,172)( 57,174)
( 58,173)( 59,167)( 60,168)( 61,170)( 62,169)( 63,203)( 64,204)( 65,206)
( 66,205)( 67,219)( 68,220)( 69,222)( 70,221)( 71,215)( 72,216)( 73,218)
( 74,217)( 75,211)( 76,212)( 77,214)( 78,213)( 79,207)( 80,208)( 81,210)
( 82,209)( 83,183)( 84,184)( 85,186)( 86,185)( 87,199)( 88,200)( 89,202)
( 90,201)( 91,195)( 92,196)( 93,198)( 94,197)( 95,191)( 96,192)( 97,194)
( 98,193)( 99,187)(100,188)(101,190)(102,189)(103,223)(104,224)(105,226)
(106,225)(107,239)(108,240)(109,242)(110,241)(111,235)(112,236)(113,238)
(114,237)(115,231)(116,232)(117,234)(118,233)(119,227)(120,228)(121,230)
(122,229);
s3 := Sym(242)!( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 11, 22)( 12, 21)( 13, 20)
( 14, 19)( 15, 18)( 16, 17)( 23, 30)( 24, 29)( 25, 28)( 26, 27)( 31, 42)
( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 63, 70)
( 64, 69)( 65, 68)( 66, 67)( 71, 82)( 72, 81)( 73, 80)( 74, 79)( 75, 78)
( 76, 77)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 91,102)( 92,101)( 93,100)
( 94, 99)( 95, 98)( 96, 97)(103,110)(104,109)(105,108)(106,107)(111,122)
(112,121)(113,120)(114,119)(115,118)(116,117)(123,130)(124,129)(125,128)
(126,127)(131,142)(132,141)(133,140)(134,139)(135,138)(136,137)(143,150)
(144,149)(145,148)(146,147)(151,162)(152,161)(153,160)(154,159)(155,158)
(156,157)(163,170)(164,169)(165,168)(166,167)(171,182)(172,181)(173,180)
(174,179)(175,178)(176,177)(183,190)(184,189)(185,188)(186,187)(191,202)
(192,201)(193,200)(194,199)(195,198)(196,197)(203,210)(204,209)(205,208)
(206,207)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,230)
(224,229)(225,228)(226,227)(231,242)(232,241)(233,240)(234,239)(235,238)
(236,237);
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*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*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 >;
to this polytope