Polytope of Type {2,12,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,151321)
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 : {2,12,20}*960
3-fold quotients : {2,4,20}*640
4-fold quotients : {2,12,10}*480, {2,6,20}*480a
5-fold quotients : {2,12,4}*384a
6-fold quotients : {2,4,20}*320
8-fold quotients : {2,6,10}*240
10-fold quotients : {2,12,4}*192a
12-fold quotients : {2,2,20}*160, {2,4,10}*160
15-fold quotients : {2,4,4}*128
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
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)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 63, 78)( 64, 79)( 65, 80)( 66, 81)
( 67, 82)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)( 74, 84)
( 75, 85)( 76, 86)( 77, 87)( 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)
(183,228)(184,229)(185,230)(186,231)(187,232)(188,238)(189,239)(190,240)
(191,241)(192,242)(193,233)(194,234)(195,235)(196,236)(197,237)(198,213)
(199,214)(200,215)(201,216)(202,217)(203,223)(204,224)(205,225)(206,226)
(207,227)(208,218)(209,219)(210,220)(211,221)(212,222);;
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)( 33,158)( 34,162)
( 35,161)( 36,160)( 37,159)( 38,153)( 39,157)( 40,156)( 41,155)( 42,154)
( 43,163)( 44,167)( 45,166)( 46,165)( 47,164)( 48,173)( 49,177)( 50,176)
( 51,175)( 52,174)( 53,168)( 54,172)( 55,171)( 56,170)( 57,169)( 58,178)
( 59,182)( 60,181)( 61,180)( 62,179)( 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)( 93,218)( 94,222)( 95,221)( 96,220)( 97,219)( 98,213)
( 99,217)(100,216)(101,215)(102,214)(103,223)(104,227)(105,226)(106,225)
(107,224)(108,233)(109,237)(110,236)(111,235)(112,234)(113,228)(114,232)
(115,231)(116,230)(117,229)(118,238)(119,242)(120,241)(121,240)(122,239);;
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, 49)( 34, 48)( 35, 52)( 36, 51)
( 37, 50)( 38, 54)( 39, 53)( 40, 57)( 41, 56)( 42, 55)( 43, 59)( 44, 58)
( 45, 62)( 46, 61)( 47, 60)( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)
( 75, 77)( 78, 79)( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93,109)
( 94,108)( 95,112)( 96,111)( 97,110)( 98,114)( 99,113)(100,117)(101,116)
(102,115)(103,119)(104,118)(105,122)(106,121)(107,120)(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)(153,229)(154,228)(155,232)(156,231)
(157,230)(158,234)(159,233)(160,237)(161,236)(162,235)(163,239)(164,238)
(165,242)(166,241)(167,240)(168,214)(169,213)(170,217)(171,216)(172,215)
(173,219)(174,218)(175,222)(176,221)(177,220)(178,224)(179,223)(180,227)
(181,226)(182,225);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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)!( 8, 13)( 9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 63, 78)( 64, 79)( 65, 80)
( 66, 81)( 67, 82)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)( 73, 83)
( 74, 84)( 75, 85)( 76, 86)( 77, 87)( 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)(183,228)(184,229)(185,230)(186,231)(187,232)(188,238)(189,239)
(190,240)(191,241)(192,242)(193,233)(194,234)(195,235)(196,236)(197,237)
(198,213)(199,214)(200,215)(201,216)(202,217)(203,223)(204,224)(205,225)
(206,226)(207,227)(208,218)(209,219)(210,220)(211,221)(212,222);
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)( 33,158)
( 34,162)( 35,161)( 36,160)( 37,159)( 38,153)( 39,157)( 40,156)( 41,155)
( 42,154)( 43,163)( 44,167)( 45,166)( 46,165)( 47,164)( 48,173)( 49,177)
( 50,176)( 51,175)( 52,174)( 53,168)( 54,172)( 55,171)( 56,170)( 57,169)
( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 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)( 93,218)( 94,222)( 95,221)( 96,220)( 97,219)
( 98,213)( 99,217)(100,216)(101,215)(102,214)(103,223)(104,227)(105,226)
(106,225)(107,224)(108,233)(109,237)(110,236)(111,235)(112,234)(113,228)
(114,232)(115,231)(116,230)(117,229)(118,238)(119,242)(120,241)(121,240)
(122,239);
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, 49)( 34, 48)( 35, 52)
( 36, 51)( 37, 50)( 38, 54)( 39, 53)( 40, 57)( 41, 56)( 42, 55)( 43, 59)
( 44, 58)( 45, 62)( 46, 61)( 47, 60)( 63, 64)( 65, 67)( 68, 69)( 70, 72)
( 73, 74)( 75, 77)( 78, 79)( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)
( 93,109)( 94,108)( 95,112)( 96,111)( 97,110)( 98,114)( 99,113)(100,117)
(101,116)(102,115)(103,119)(104,118)(105,122)(106,121)(107,120)(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)(153,229)(154,228)(155,232)
(156,231)(157,230)(158,234)(159,233)(160,237)(161,236)(162,235)(163,239)
(164,238)(165,242)(166,241)(167,240)(168,214)(169,213)(170,217)(171,216)
(172,215)(173,219)(174,218)(175,222)(176,221)(177,220)(178,224)(179,223)
(180,227)(181,226)(182,225);
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope