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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,30,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 5
Schlafli Type : {2,4,30,2}
Number of vertices, edges, etc : 2, 8, 120, 60, 2
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 : {2,4,15,2}*960, {2,4,30,2}*960b, {2,4,30,2}*960c
   4-fold quotients : {2,4,15,2}*480, {2,2,30,2}*480
   5-fold quotients : {2,4,6,2}*384
   8-fold quotients : {2,2,15,2}*240
   10-fold quotients : {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
   12-fold quotients : {2,2,10,2}*160
   20-fold quotients : {2,4,3,2}*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 := (  3,125)(  4,126)(  5,123)(  6,124)(  7,129)(  8,130)(  9,127)( 10,128)
( 11,133)( 12,134)( 13,131)( 14,132)( 15,137)( 16,138)( 17,135)( 18,136)
( 19,141)( 20,142)( 21,139)( 22,140)( 23,145)( 24,146)( 25,143)( 26,144)
( 27,149)( 28,150)( 29,147)( 30,148)( 31,153)( 32,154)( 33,151)( 34,152)
( 35,157)( 36,158)( 37,155)( 38,156)( 39,161)( 40,162)( 41,159)( 42,160)
( 43,165)( 44,166)( 45,163)( 46,164)( 47,169)( 48,170)( 49,167)( 50,168)
( 51,173)( 52,174)( 53,171)( 54,172)( 55,177)( 56,178)( 57,175)( 58,176)
( 59,181)( 60,182)( 61,179)( 62,180)( 63,185)( 64,186)( 65,183)( 66,184)
( 67,189)( 68,190)( 69,187)( 70,188)( 71,193)( 72,194)( 73,191)( 74,192)
( 75,197)( 76,198)( 77,195)( 78,196)( 79,201)( 80,202)( 81,199)( 82,200)
( 83,205)( 84,206)( 85,203)( 86,204)( 87,209)( 88,210)( 89,207)( 90,208)
( 91,213)( 92,214)( 93,211)( 94,212)( 95,217)( 96,218)( 97,215)( 98,216)
( 99,221)(100,222)(101,219)(102,220)(103,225)(104,226)(105,223)(106,224)
(107,229)(108,230)(109,227)(110,228)(111,233)(112,234)(113,231)(114,232)
(115,237)(116,238)(117,235)(118,236)(119,241)(120,242)(121,239)(122,240);;
s2 := (  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)
( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)
( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)
( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)
( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)
( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)
(101,108)(102,110)(124,125)(127,139)(128,141)(129,140)(130,142)(131,135)
(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)(147,179)
(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)(155,171)
(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)(184,185)
(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)(194,198)
(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)(210,242)
(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)
(219,227)(220,229)(221,228)(222,230);;
s3 := (  3,107)(  4,110)(  5,109)(  6,108)(  7,103)(  8,106)(  9,105)( 10,104)
( 11,119)( 12,122)( 13,121)( 14,120)( 15,115)( 16,118)( 17,117)( 18,116)
( 19,111)( 20,114)( 21,113)( 22,112)( 23, 87)( 24, 90)( 25, 89)( 26, 88)
( 27, 83)( 28, 86)( 29, 85)( 30, 84)( 31, 99)( 32,102)( 33,101)( 34,100)
( 35, 95)( 36, 98)( 37, 97)( 38, 96)( 39, 91)( 40, 94)( 41, 93)( 42, 92)
( 43, 67)( 44, 70)( 45, 69)( 46, 68)( 47, 63)( 48, 66)( 49, 65)( 50, 64)
( 51, 79)( 52, 82)( 53, 81)( 54, 80)( 55, 75)( 56, 78)( 57, 77)( 58, 76)
( 59, 71)( 60, 74)( 61, 73)( 62, 72)(123,227)(124,230)(125,229)(126,228)
(127,223)(128,226)(129,225)(130,224)(131,239)(132,242)(133,241)(134,240)
(135,235)(136,238)(137,237)(138,236)(139,231)(140,234)(141,233)(142,232)
(143,207)(144,210)(145,209)(146,208)(147,203)(148,206)(149,205)(150,204)
(151,219)(152,222)(153,221)(154,220)(155,215)(156,218)(157,217)(158,216)
(159,211)(160,214)(161,213)(162,212)(163,187)(164,190)(165,189)(166,188)
(167,183)(168,186)(169,185)(170,184)(171,199)(172,202)(173,201)(174,200)
(175,195)(176,198)(177,197)(178,196)(179,191)(180,194)(181,193)(182,192);;
s4 := (243,244);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*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*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)!(  3,125)(  4,126)(  5,123)(  6,124)(  7,129)(  8,130)(  9,127)
( 10,128)( 11,133)( 12,134)( 13,131)( 14,132)( 15,137)( 16,138)( 17,135)
( 18,136)( 19,141)( 20,142)( 21,139)( 22,140)( 23,145)( 24,146)( 25,143)
( 26,144)( 27,149)( 28,150)( 29,147)( 30,148)( 31,153)( 32,154)( 33,151)
( 34,152)( 35,157)( 36,158)( 37,155)( 38,156)( 39,161)( 40,162)( 41,159)
( 42,160)( 43,165)( 44,166)( 45,163)( 46,164)( 47,169)( 48,170)( 49,167)
( 50,168)( 51,173)( 52,174)( 53,171)( 54,172)( 55,177)( 56,178)( 57,175)
( 58,176)( 59,181)( 60,182)( 61,179)( 62,180)( 63,185)( 64,186)( 65,183)
( 66,184)( 67,189)( 68,190)( 69,187)( 70,188)( 71,193)( 72,194)( 73,191)
( 74,192)( 75,197)( 76,198)( 77,195)( 78,196)( 79,201)( 80,202)( 81,199)
( 82,200)( 83,205)( 84,206)( 85,203)( 86,204)( 87,209)( 88,210)( 89,207)
( 90,208)( 91,213)( 92,214)( 93,211)( 94,212)( 95,217)( 96,218)( 97,215)
( 98,216)( 99,221)(100,222)(101,219)(102,220)(103,225)(104,226)(105,223)
(106,224)(107,229)(108,230)(109,227)(110,228)(111,233)(112,234)(113,231)
(114,232)(115,237)(116,238)(117,235)(118,236)(119,241)(120,242)(121,239)
(122,240);
s2 := Sym(244)!(  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)
( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)
( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)
( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)
( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)
( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)
(100,109)(101,108)(102,110)(124,125)(127,139)(128,141)(129,140)(130,142)
(131,135)(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)
(147,179)(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)
(155,171)(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)
(184,185)(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)
(194,198)(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)
(210,242)(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)
(218,234)(219,227)(220,229)(221,228)(222,230);
s3 := Sym(244)!(  3,107)(  4,110)(  5,109)(  6,108)(  7,103)(  8,106)(  9,105)
( 10,104)( 11,119)( 12,122)( 13,121)( 14,120)( 15,115)( 16,118)( 17,117)
( 18,116)( 19,111)( 20,114)( 21,113)( 22,112)( 23, 87)( 24, 90)( 25, 89)
( 26, 88)( 27, 83)( 28, 86)( 29, 85)( 30, 84)( 31, 99)( 32,102)( 33,101)
( 34,100)( 35, 95)( 36, 98)( 37, 97)( 38, 96)( 39, 91)( 40, 94)( 41, 93)
( 42, 92)( 43, 67)( 44, 70)( 45, 69)( 46, 68)( 47, 63)( 48, 66)( 49, 65)
( 50, 64)( 51, 79)( 52, 82)( 53, 81)( 54, 80)( 55, 75)( 56, 78)( 57, 77)
( 58, 76)( 59, 71)( 60, 74)( 61, 73)( 62, 72)(123,227)(124,230)(125,229)
(126,228)(127,223)(128,226)(129,225)(130,224)(131,239)(132,242)(133,241)
(134,240)(135,235)(136,238)(137,237)(138,236)(139,231)(140,234)(141,233)
(142,232)(143,207)(144,210)(145,209)(146,208)(147,203)(148,206)(149,205)
(150,204)(151,219)(152,222)(153,221)(154,220)(155,215)(156,218)(157,217)
(158,216)(159,211)(160,214)(161,213)(162,212)(163,187)(164,190)(165,189)
(166,188)(167,183)(168,186)(169,185)(170,184)(171,199)(172,202)(173,201)
(174,200)(175,195)(176,198)(177,197)(178,196)(179,191)(180,194)(181,193)
(182,192);
s4 := Sym(244)!(243,244);
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope