Polytope of Type {2,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 4
Schlafli Type : {2,30,4}
Number of vertices, edges, etc : 2, 120, 240, 16
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 : {2,30,4}*960
   4-fold quotients : {2,30,4}*480a, {2,15,4}*480, {2,30,4}*480b, {2,30,4}*480c
   5-fold quotients : {2,6,4}*384b
   8-fold quotients : {2,15,4}*240, {2,30,2}*240
   10-fold quotients : {2,6,4}*192
   12-fold quotients : {2,10,4}*160
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,6,4}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {2,3,4}*48, {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*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 := (  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);;
s2 := (  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 23)(  8, 24)(  9, 26)( 10, 25)
( 11, 39)( 12, 40)( 13, 42)( 14, 41)( 15, 35)( 16, 36)( 17, 38)( 18, 37)
( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 43, 47)( 44, 48)( 45, 50)( 46, 49)
( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 57, 58)( 63, 87)( 64, 88)( 65, 90)
( 66, 89)( 67, 83)( 68, 84)( 69, 86)( 70, 85)( 71, 99)( 72,100)( 73,102)
( 74,101)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 91)( 80, 92)( 81, 94)
( 82, 93)(103,107)(104,108)(105,110)(106,109)(111,119)(112,120)(113,122)
(114,121)(117,118)(123,207)(124,208)(125,210)(126,209)(127,203)(128,204)
(129,206)(130,205)(131,219)(132,220)(133,222)(134,221)(135,215)(136,216)
(137,218)(138,217)(139,211)(140,212)(141,214)(142,213)(143,187)(144,188)
(145,190)(146,189)(147,183)(148,184)(149,186)(150,185)(151,199)(152,200)
(153,202)(154,201)(155,195)(156,196)(157,198)(158,197)(159,191)(160,192)
(161,194)(162,193)(163,227)(164,228)(165,230)(166,229)(167,223)(168,224)
(169,226)(170,225)(171,239)(172,240)(173,242)(174,241)(175,235)(176,236)
(177,238)(178,237)(179,231)(180,232)(181,234)(182,233);;
s3 := (  3,126)(  4,125)(  5,124)(  6,123)(  7,130)(  8,129)(  9,128)( 10,127)
( 11,134)( 12,133)( 13,132)( 14,131)( 15,138)( 16,137)( 17,136)( 18,135)
( 19,142)( 20,141)( 21,140)( 22,139)( 23,146)( 24,145)( 25,144)( 26,143)
( 27,150)( 28,149)( 29,148)( 30,147)( 31,154)( 32,153)( 33,152)( 34,151)
( 35,158)( 36,157)( 37,156)( 38,155)( 39,162)( 40,161)( 41,160)( 42,159)
( 43,166)( 44,165)( 45,164)( 46,163)( 47,170)( 48,169)( 49,168)( 50,167)
( 51,174)( 52,173)( 53,172)( 54,171)( 55,178)( 56,177)( 57,176)( 58,175)
( 59,182)( 60,181)( 61,180)( 62,179)( 63,186)( 64,185)( 65,184)( 66,183)
( 67,190)( 68,189)( 69,188)( 70,187)( 71,194)( 72,193)( 73,192)( 74,191)
( 75,198)( 76,197)( 77,196)( 78,195)( 79,202)( 80,201)( 81,200)( 82,199)
( 83,206)( 84,205)( 85,204)( 86,203)( 87,210)( 88,209)( 89,208)( 90,207)
( 91,214)( 92,213)( 93,212)( 94,211)( 95,218)( 96,217)( 97,216)( 98,215)
( 99,222)(100,221)(101,220)(102,219)(103,226)(104,225)(105,224)(106,223)
(107,230)(108,229)(109,228)(110,227)(111,234)(112,233)(113,232)(114,231)
(115,238)(116,237)(117,236)(118,235)(119,242)(120,241)(121,240)(122,239);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope