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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 5
Schlafli Type : {30,4,2,2}
Number of vertices, edges, etc : 60, 120, 8, 2, 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 : {15,4,2,2}*960, {30,4,2,2}*960b, {30,4,2,2}*960c
   4-fold quotients : {15,4,2,2}*480, {30,2,2,2}*480
   5-fold quotients : {6,4,2,2}*384
   8-fold quotients : {15,2,2,2}*240
   10-fold quotients : {3,4,2,2}*192, {6,4,2,2}*192b, {6,4,2,2}*192c
   12-fold quotients : {10,2,2,2}*160
   20-fold quotients : {3,4,2,2}*96, {6,2,2,2}*96
   24-fold quotients : {5,2,2,2}*80
   40-fold quotients : {3,2,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope