Polytope of Type {2,2,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,30}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 5
Schlafli Type : {2,2,4,30}
Number of vertices, edges, etc : 2, 2, 8, 120, 60
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 : {2,2,4,15}*960, {2,2,4,30}*960b, {2,2,4,30}*960c
   4-fold quotients : {2,2,4,15}*480, {2,2,2,30}*480
   5-fold quotients : {2,2,4,6}*384
   8-fold quotients : {2,2,2,15}*240
   10-fold quotients : {2,2,4,3}*192, {2,2,4,6}*192b, {2,2,4,6}*192c
   12-fold quotients : {2,2,2,10}*160
   20-fold quotients : {2,2,4,3}*96, {2,2,2,6}*96
   24-fold quotients : {2,2,2,5}*80
   40-fold quotients : {2,2,2,3}*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 := (  5,127)(  6,128)(  7,125)(  8,126)(  9,131)( 10,132)( 11,129)( 12,130)
( 13,135)( 14,136)( 15,133)( 16,134)( 17,139)( 18,140)( 19,137)( 20,138)
( 21,143)( 22,144)( 23,141)( 24,142)( 25,147)( 26,148)( 27,145)( 28,146)
( 29,151)( 30,152)( 31,149)( 32,150)( 33,155)( 34,156)( 35,153)( 36,154)
( 37,159)( 38,160)( 39,157)( 40,158)( 41,163)( 42,164)( 43,161)( 44,162)
( 45,167)( 46,168)( 47,165)( 48,166)( 49,171)( 50,172)( 51,169)( 52,170)
( 53,175)( 54,176)( 55,173)( 56,174)( 57,179)( 58,180)( 59,177)( 60,178)
( 61,183)( 62,184)( 63,181)( 64,182)( 65,187)( 66,188)( 67,185)( 68,186)
( 69,191)( 70,192)( 71,189)( 72,190)( 73,195)( 74,196)( 75,193)( 76,194)
( 77,199)( 78,200)( 79,197)( 80,198)( 81,203)( 82,204)( 83,201)( 84,202)
( 85,207)( 86,208)( 87,205)( 88,206)( 89,211)( 90,212)( 91,209)( 92,210)
( 93,215)( 94,216)( 95,213)( 96,214)( 97,219)( 98,220)( 99,217)(100,218)
(101,223)(102,224)(103,221)(104,222)(105,227)(106,228)(107,225)(108,226)
(109,231)(110,232)(111,229)(112,230)(113,235)(114,236)(115,233)(116,234)
(117,239)(118,240)(119,237)(120,238)(121,243)(122,244)(123,241)(124,242);;
s3 := (  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);;
s4 := (  5,109)(  6,112)(  7,111)(  8,110)(  9,105)( 10,108)( 11,107)( 12,106)
( 13,121)( 14,124)( 15,123)( 16,122)( 17,117)( 18,120)( 19,119)( 20,118)
( 21,113)( 22,116)( 23,115)( 24,114)( 25, 89)( 26, 92)( 27, 91)( 28, 90)
( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,101)( 34,104)( 35,103)( 36,102)
( 37, 97)( 38,100)( 39, 99)( 40, 98)( 41, 93)( 42, 96)( 43, 95)( 44, 94)
( 45, 69)( 46, 72)( 47, 71)( 48, 70)( 49, 65)( 50, 68)( 51, 67)( 52, 66)
( 53, 81)( 54, 84)( 55, 83)( 56, 82)( 57, 77)( 58, 80)( 59, 79)( 60, 78)
( 61, 73)( 62, 76)( 63, 75)( 64, 74)(125,229)(126,232)(127,231)(128,230)
(129,225)(130,228)(131,227)(132,226)(133,241)(134,244)(135,243)(136,242)
(137,237)(138,240)(139,239)(140,238)(141,233)(142,236)(143,235)(144,234)
(145,209)(146,212)(147,211)(148,210)(149,205)(150,208)(151,207)(152,206)
(153,221)(154,224)(155,223)(156,222)(157,217)(158,220)(159,219)(160,218)
(161,213)(162,216)(163,215)(164,214)(165,189)(166,192)(167,191)(168,190)
(169,185)(170,188)(171,187)(172,186)(173,201)(174,204)(175,203)(176,202)
(177,197)(178,200)(179,199)(180,198)(181,193)(182,196)(183,195)(184,194);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(244)!(1,2);
s1 := Sym(244)!(3,4);
s2 := Sym(244)!(  5,127)(  6,128)(  7,125)(  8,126)(  9,131)( 10,132)( 11,129)
( 12,130)( 13,135)( 14,136)( 15,133)( 16,134)( 17,139)( 18,140)( 19,137)
( 20,138)( 21,143)( 22,144)( 23,141)( 24,142)( 25,147)( 26,148)( 27,145)
( 28,146)( 29,151)( 30,152)( 31,149)( 32,150)( 33,155)( 34,156)( 35,153)
( 36,154)( 37,159)( 38,160)( 39,157)( 40,158)( 41,163)( 42,164)( 43,161)
( 44,162)( 45,167)( 46,168)( 47,165)( 48,166)( 49,171)( 50,172)( 51,169)
( 52,170)( 53,175)( 54,176)( 55,173)( 56,174)( 57,179)( 58,180)( 59,177)
( 60,178)( 61,183)( 62,184)( 63,181)( 64,182)( 65,187)( 66,188)( 67,185)
( 68,186)( 69,191)( 70,192)( 71,189)( 72,190)( 73,195)( 74,196)( 75,193)
( 76,194)( 77,199)( 78,200)( 79,197)( 80,198)( 81,203)( 82,204)( 83,201)
( 84,202)( 85,207)( 86,208)( 87,205)( 88,206)( 89,211)( 90,212)( 91,209)
( 92,210)( 93,215)( 94,216)( 95,213)( 96,214)( 97,219)( 98,220)( 99,217)
(100,218)(101,223)(102,224)(103,221)(104,222)(105,227)(106,228)(107,225)
(108,226)(109,231)(110,232)(111,229)(112,230)(113,235)(114,236)(115,233)
(116,234)(117,239)(118,240)(119,237)(120,238)(121,243)(122,244)(123,241)
(124,242);
s3 := 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);
s4 := Sym(244)!(  5,109)(  6,112)(  7,111)(  8,110)(  9,105)( 10,108)( 11,107)
( 12,106)( 13,121)( 14,124)( 15,123)( 16,122)( 17,117)( 18,120)( 19,119)
( 20,118)( 21,113)( 22,116)( 23,115)( 24,114)( 25, 89)( 26, 92)( 27, 91)
( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,101)( 34,104)( 35,103)
( 36,102)( 37, 97)( 38,100)( 39, 99)( 40, 98)( 41, 93)( 42, 96)( 43, 95)
( 44, 94)( 45, 69)( 46, 72)( 47, 71)( 48, 70)( 49, 65)( 50, 68)( 51, 67)
( 52, 66)( 53, 81)( 54, 84)( 55, 83)( 56, 82)( 57, 77)( 58, 80)( 59, 79)
( 60, 78)( 61, 73)( 62, 76)( 63, 75)( 64, 74)(125,229)(126,232)(127,231)
(128,230)(129,225)(130,228)(131,227)(132,226)(133,241)(134,244)(135,243)
(136,242)(137,237)(138,240)(139,239)(140,238)(141,233)(142,236)(143,235)
(144,234)(145,209)(146,212)(147,211)(148,210)(149,205)(150,208)(151,207)
(152,206)(153,221)(154,224)(155,223)(156,222)(157,217)(158,220)(159,219)
(160,218)(161,213)(162,216)(163,215)(164,214)(165,189)(166,192)(167,191)
(168,190)(169,185)(170,188)(171,187)(172,186)(173,201)(174,204)(175,203)
(176,202)(177,197)(178,200)(179,199)(180,198)(181,193)(182,196)(183,195)
(184,194);
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope