Polytope of Type {2,2,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,30,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 5
Schlafli Type : {2,2,30,4}
Number of vertices, edges, etc : 2, 2, 60, 120, 8
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,15,4}*960, {2,2,30,4}*960b, {2,2,30,4}*960c
4-fold quotients : {2,2,15,4}*480, {2,2,30,2}*480
5-fold quotients : {2,2,6,4}*384
8-fold quotients : {2,2,15,2}*240
10-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
12-fold quotients : {2,2,10,2}*160
20-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
24-fold quotients : {2,2,5,2}*80
40-fold quotients : {2,2,3,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)( 15, 18)
( 16, 20)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 61)( 30, 63)( 31, 62)
( 32, 64)( 33, 57)( 34, 59)( 35, 58)( 36, 60)( 37, 53)( 38, 55)( 39, 54)
( 40, 56)( 41, 49)( 42, 51)( 43, 50)( 44, 52)( 66, 67)( 69, 81)( 70, 83)
( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80)( 85,105)( 86,107)
( 87,106)( 88,108)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)( 94,119)
( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)(102,111)
(103,110)(104,112)(126,127)(129,141)(130,143)(131,142)(132,144)(133,137)
(134,139)(135,138)(136,140)(145,165)(146,167)(147,166)(148,168)(149,181)
(150,183)(151,182)(152,184)(153,177)(154,179)(155,178)(156,180)(157,173)
(158,175)(159,174)(160,176)(161,169)(162,171)(163,170)(164,172)(186,187)
(189,201)(190,203)(191,202)(192,204)(193,197)(194,199)(195,198)(196,200)
(205,225)(206,227)(207,226)(208,228)(209,241)(210,243)(211,242)(212,244)
(213,237)(214,239)(215,238)(216,240)(217,233)(218,235)(219,234)(220,236)
(221,229)(222,231)(223,230)(224,232);;
s3 := ( 5,149)( 6,150)( 7,152)( 8,151)( 9,145)( 10,146)( 11,148)( 12,147)
( 13,161)( 14,162)( 15,164)( 16,163)( 17,157)( 18,158)( 19,160)( 20,159)
( 21,153)( 22,154)( 23,156)( 24,155)( 25,129)( 26,130)( 27,132)( 28,131)
( 29,125)( 30,126)( 31,128)( 32,127)( 33,141)( 34,142)( 35,144)( 36,143)
( 37,137)( 38,138)( 39,140)( 40,139)( 41,133)( 42,134)( 43,136)( 44,135)
( 45,169)( 46,170)( 47,172)( 48,171)( 49,165)( 50,166)( 51,168)( 52,167)
( 53,181)( 54,182)( 55,184)( 56,183)( 57,177)( 58,178)( 59,180)( 60,179)
( 61,173)( 62,174)( 63,176)( 64,175)( 65,209)( 66,210)( 67,212)( 68,211)
( 69,205)( 70,206)( 71,208)( 72,207)( 73,221)( 74,222)( 75,224)( 76,223)
( 77,217)( 78,218)( 79,220)( 80,219)( 81,213)( 82,214)( 83,216)( 84,215)
( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)
( 93,201)( 94,202)( 95,204)( 96,203)( 97,197)( 98,198)( 99,200)(100,199)
(101,193)(102,194)(103,196)(104,195)(105,229)(106,230)(107,232)(108,231)
(109,225)(110,226)(111,228)(112,227)(113,241)(114,242)(115,244)(116,243)
(117,237)(118,238)(119,240)(120,239)(121,233)(122,234)(123,236)(124,235);;
s4 := ( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 72)( 10, 71)( 11, 70)( 12, 69)
( 13, 76)( 14, 75)( 15, 74)( 16, 73)( 17, 80)( 18, 79)( 19, 78)( 20, 77)
( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 88)( 26, 87)( 27, 86)( 28, 85)
( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 96)( 34, 95)( 35, 94)( 36, 93)
( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41,104)( 42,103)( 43,102)( 44,101)
( 45,108)( 46,107)( 47,106)( 48,105)( 49,112)( 50,111)( 51,110)( 52,109)
( 53,116)( 54,115)( 55,114)( 56,113)( 57,120)( 58,119)( 59,118)( 60,117)
( 61,124)( 62,123)( 63,122)( 64,121)(125,188)(126,187)(127,186)(128,185)
(129,192)(130,191)(131,190)(132,189)(133,196)(134,195)(135,194)(136,193)
(137,200)(138,199)(139,198)(140,197)(141,204)(142,203)(143,202)(144,201)
(145,208)(146,207)(147,206)(148,205)(149,212)(150,211)(151,210)(152,209)
(153,216)(154,215)(155,214)(156,213)(157,220)(158,219)(159,218)(160,217)
(161,224)(162,223)(163,222)(164,221)(165,228)(166,227)(167,226)(168,225)
(169,232)(170,231)(171,230)(172,229)(173,236)(174,235)(175,234)(176,233)
(177,240)(178,239)(179,238)(180,237)(181,244)(182,243)(183,242)(184,241);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s2*s3*s4*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*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(244)!(1,2);
s1 := Sym(244)!(3,4);
s2 := Sym(244)!( 6, 7)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)
( 15, 18)( 16, 20)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 61)( 30, 63)
( 31, 62)( 32, 64)( 33, 57)( 34, 59)( 35, 58)( 36, 60)( 37, 53)( 38, 55)
( 39, 54)( 40, 56)( 41, 49)( 42, 51)( 43, 50)( 44, 52)( 66, 67)( 69, 81)
( 70, 83)( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80)( 85,105)
( 86,107)( 87,106)( 88,108)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)
( 94,119)( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)
(102,111)(103,110)(104,112)(126,127)(129,141)(130,143)(131,142)(132,144)
(133,137)(134,139)(135,138)(136,140)(145,165)(146,167)(147,166)(148,168)
(149,181)(150,183)(151,182)(152,184)(153,177)(154,179)(155,178)(156,180)
(157,173)(158,175)(159,174)(160,176)(161,169)(162,171)(163,170)(164,172)
(186,187)(189,201)(190,203)(191,202)(192,204)(193,197)(194,199)(195,198)
(196,200)(205,225)(206,227)(207,226)(208,228)(209,241)(210,243)(211,242)
(212,244)(213,237)(214,239)(215,238)(216,240)(217,233)(218,235)(219,234)
(220,236)(221,229)(222,231)(223,230)(224,232);
s3 := Sym(244)!( 5,149)( 6,150)( 7,152)( 8,151)( 9,145)( 10,146)( 11,148)
( 12,147)( 13,161)( 14,162)( 15,164)( 16,163)( 17,157)( 18,158)( 19,160)
( 20,159)( 21,153)( 22,154)( 23,156)( 24,155)( 25,129)( 26,130)( 27,132)
( 28,131)( 29,125)( 30,126)( 31,128)( 32,127)( 33,141)( 34,142)( 35,144)
( 36,143)( 37,137)( 38,138)( 39,140)( 40,139)( 41,133)( 42,134)( 43,136)
( 44,135)( 45,169)( 46,170)( 47,172)( 48,171)( 49,165)( 50,166)( 51,168)
( 52,167)( 53,181)( 54,182)( 55,184)( 56,183)( 57,177)( 58,178)( 59,180)
( 60,179)( 61,173)( 62,174)( 63,176)( 64,175)( 65,209)( 66,210)( 67,212)
( 68,211)( 69,205)( 70,206)( 71,208)( 72,207)( 73,221)( 74,222)( 75,224)
( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,213)( 82,214)( 83,216)
( 84,215)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)
( 92,187)( 93,201)( 94,202)( 95,204)( 96,203)( 97,197)( 98,198)( 99,200)
(100,199)(101,193)(102,194)(103,196)(104,195)(105,229)(106,230)(107,232)
(108,231)(109,225)(110,226)(111,228)(112,227)(113,241)(114,242)(115,244)
(116,243)(117,237)(118,238)(119,240)(120,239)(121,233)(122,234)(123,236)
(124,235);
s4 := Sym(244)!( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 72)( 10, 71)( 11, 70)
( 12, 69)( 13, 76)( 14, 75)( 15, 74)( 16, 73)( 17, 80)( 18, 79)( 19, 78)
( 20, 77)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 88)( 26, 87)( 27, 86)
( 28, 85)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 96)( 34, 95)( 35, 94)
( 36, 93)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41,104)( 42,103)( 43,102)
( 44,101)( 45,108)( 46,107)( 47,106)( 48,105)( 49,112)( 50,111)( 51,110)
( 52,109)( 53,116)( 54,115)( 55,114)( 56,113)( 57,120)( 58,119)( 59,118)
( 60,117)( 61,124)( 62,123)( 63,122)( 64,121)(125,188)(126,187)(127,186)
(128,185)(129,192)(130,191)(131,190)(132,189)(133,196)(134,195)(135,194)
(136,193)(137,200)(138,199)(139,198)(140,197)(141,204)(142,203)(143,202)
(144,201)(145,208)(146,207)(147,206)(148,205)(149,212)(150,211)(151,210)
(152,209)(153,216)(154,215)(155,214)(156,213)(157,220)(158,219)(159,218)
(160,217)(161,224)(162,223)(163,222)(164,221)(165,228)(166,227)(167,226)
(168,225)(169,232)(170,231)(171,230)(172,229)(173,236)(174,235)(175,234)
(176,233)(177,240)(178,239)(179,238)(180,237)(181,244)(182,243)(183,242)
(184,241);
poly := sub<Sym(244)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*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*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