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