Polytope of Type {4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30}*480
if this polytope has a name.
Group : SmallGroup(480,1199)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 8, 120, 60
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,30,2} of size 960
   {4,30,4} of size 1920
   {4,30,4} of size 1920
   {4,30,4} of size 1920
Vertex Figure Of :
   {2,4,30} of size 960
   {4,4,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   4-fold quotients : {4,15}*120, {2,30}*120
   5-fold quotients : {4,6}*96
   8-fold quotients : {2,15}*60
   10-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   12-fold quotients : {2,10}*40
   20-fold quotients : {4,3}*24, {2,6}*24
   24-fold quotients : {2,5}*20
   40-fold quotients : {2,3}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c
   3-fold covers : {4,90}*1440, {12,30}*1440a, {12,30}*1440b
   4-fold covers : {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,30}*1920a, {8,30}*1920d, {8,30}*1920e, {8,30}*1920f, {8,60}*1920g, {8,60}*1920h, {4,120}*1920c, {4,120}*1920d, {8,30}*1920g, {4,60}*1920e, {4,120}*1920e, {4,30}*1920b, {4,120}*1920f
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
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 >;

References : None.
to this polytope