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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,30,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208103)
Rank : 5
Schlafli Type : {2,4,30,4}
Number of vertices, edges, etc : 2, 4, 60, 60, 4
Order of s₀s₁s₂s₃s₄ : 60
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 : {2,2,30,4}*960a, {2,4,30,2}*960a
   3-fold quotients : {2,4,10,4}*640
   4-fold quotients : {2,2,30,2}*480
   5-fold quotients : {2,4,6,4}*384a
   6-fold quotients : {2,2,10,4}*320, {2,4,10,2}*320
   8-fold quotients : {2,2,15,2}*240
   10-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a
   12-fold quotients : {2,2,10,2}*160
   15-fold quotients : {2,4,2,4}*128
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   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 := (123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)
(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)(138,168)
(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)(146,176)
(147,177)(148,178)(149,179)(150,180)(151,181)(152,182)(183,213)(184,214)
(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)(191,221)(192,222)
(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)
(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)(208,238)
(209,239)(210,240)(211,241)(212,242);;
s2 := (  3,123)(  4,127)(  5,126)(  6,125)(  7,124)(  8,133)(  9,137)( 10,136)
( 11,135)( 12,134)( 13,128)( 14,132)( 15,131)( 16,130)( 17,129)( 18,138)
( 19,142)( 20,141)( 21,140)( 22,139)( 23,148)( 24,152)( 25,151)( 26,150)
( 27,149)( 28,143)( 29,147)( 30,146)( 31,145)( 32,144)( 33,153)( 34,157)
( 35,156)( 36,155)( 37,154)( 38,163)( 39,167)( 40,166)( 41,165)( 42,164)
( 43,158)( 44,162)( 45,161)( 46,160)( 47,159)( 48,168)( 49,172)( 50,171)
( 51,170)( 52,169)( 53,178)( 54,182)( 55,181)( 56,180)( 57,179)( 58,173)
( 59,177)( 60,176)( 61,175)( 62,174)( 63,213)( 64,217)( 65,216)( 66,215)
( 67,214)( 68,223)( 69,227)( 70,226)( 71,225)( 72,224)( 73,218)( 74,222)
( 75,221)( 76,220)( 77,219)( 78,228)( 79,232)( 80,231)( 81,230)( 82,229)
( 83,238)( 84,242)( 85,241)( 86,240)( 87,239)( 88,233)( 89,237)( 90,236)
( 91,235)( 92,234)( 93,183)( 94,187)( 95,186)( 96,185)( 97,184)( 98,193)
( 99,197)(100,196)(101,195)(102,194)(103,188)(104,192)(105,191)(106,190)
(107,189)(108,198)(109,202)(110,201)(111,200)(112,199)(113,208)(114,212)
(115,211)(116,210)(117,209)(118,203)(119,207)(120,206)(121,205)(122,204);;
s3 := (  3,  9)(  4,  8)(  5, 12)(  6, 11)(  7, 10)( 13, 14)( 15, 17)( 18, 24)
( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 29)( 30, 32)( 33, 39)( 34, 38)
( 35, 42)( 36, 41)( 37, 40)( 43, 44)( 45, 47)( 48, 54)( 49, 53)( 50, 57)
( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63,114)( 64,113)( 65,117)( 66,116)
( 67,115)( 68,109)( 69,108)( 70,112)( 71,111)( 72,110)( 73,119)( 74,118)
( 75,122)( 76,121)( 77,120)( 78, 99)( 79, 98)( 80,102)( 81,101)( 82,100)
( 83, 94)( 84, 93)( 85, 97)( 86, 96)( 87, 95)( 88,104)( 89,103)( 90,107)
( 91,106)( 92,105)(123,129)(124,128)(125,132)(126,131)(127,130)(133,134)
(135,137)(138,144)(139,143)(140,147)(141,146)(142,145)(148,149)(150,152)
(153,159)(154,158)(155,162)(156,161)(157,160)(163,164)(165,167)(168,174)
(169,173)(170,177)(171,176)(172,175)(178,179)(180,182)(183,234)(184,233)
(185,237)(186,236)(187,235)(188,229)(189,228)(190,232)(191,231)(192,230)
(193,239)(194,238)(195,242)(196,241)(197,240)(198,219)(199,218)(200,222)
(201,221)(202,220)(203,214)(204,213)(205,217)(206,216)(207,215)(208,224)
(209,223)(210,227)(211,226)(212,225);;
s4 := (  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)(  8, 68)(  9, 69)( 10, 70)
( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)( 18, 78)
( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 83)( 24, 84)( 25, 85)( 26, 86)
( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 93)( 34, 94)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 99)( 40,100)( 41,101)( 42,102)
( 43,103)( 44,104)( 45,105)( 46,106)( 47,107)( 48,108)( 49,109)( 50,110)
( 51,111)( 52,112)( 53,113)( 54,114)( 55,115)( 56,116)( 57,117)( 58,118)
( 59,119)( 60,120)( 61,121)( 62,122)(123,213)(124,214)(125,215)(126,216)
(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)
(135,225)(136,226)(137,227)(138,228)(139,229)(140,230)(141,231)(142,232)
(143,233)(144,234)(145,235)(146,236)(147,237)(148,238)(149,239)(150,240)
(151,241)(152,242)(153,183)(154,184)(155,185)(156,186)(157,187)(158,188)
(159,189)(160,190)(161,191)(162,192)(163,193)(164,194)(165,195)(166,196)
(167,197)(168,198)(169,199)(170,200)(171,201)(172,202)(173,203)(174,204)
(175,205)(176,206)(177,207)(178,208)(179,209)(180,210)(181,211)(182,212);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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(242)!(1,2);
s1 := Sym(242)!(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)
(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)(137,167)
(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)(145,175)
(146,176)(147,177)(148,178)(149,179)(150,180)(151,181)(152,182)(183,213)
(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)(191,221)
(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)
(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)(207,237)
(208,238)(209,239)(210,240)(211,241)(212,242);
s2 := Sym(242)!(  3,123)(  4,127)(  5,126)(  6,125)(  7,124)(  8,133)(  9,137)
( 10,136)( 11,135)( 12,134)( 13,128)( 14,132)( 15,131)( 16,130)( 17,129)
( 18,138)( 19,142)( 20,141)( 21,140)( 22,139)( 23,148)( 24,152)( 25,151)
( 26,150)( 27,149)( 28,143)( 29,147)( 30,146)( 31,145)( 32,144)( 33,153)
( 34,157)( 35,156)( 36,155)( 37,154)( 38,163)( 39,167)( 40,166)( 41,165)
( 42,164)( 43,158)( 44,162)( 45,161)( 46,160)( 47,159)( 48,168)( 49,172)
( 50,171)( 51,170)( 52,169)( 53,178)( 54,182)( 55,181)( 56,180)( 57,179)
( 58,173)( 59,177)( 60,176)( 61,175)( 62,174)( 63,213)( 64,217)( 65,216)
( 66,215)( 67,214)( 68,223)( 69,227)( 70,226)( 71,225)( 72,224)( 73,218)
( 74,222)( 75,221)( 76,220)( 77,219)( 78,228)( 79,232)( 80,231)( 81,230)
( 82,229)( 83,238)( 84,242)( 85,241)( 86,240)( 87,239)( 88,233)( 89,237)
( 90,236)( 91,235)( 92,234)( 93,183)( 94,187)( 95,186)( 96,185)( 97,184)
( 98,193)( 99,197)(100,196)(101,195)(102,194)(103,188)(104,192)(105,191)
(106,190)(107,189)(108,198)(109,202)(110,201)(111,200)(112,199)(113,208)
(114,212)(115,211)(116,210)(117,209)(118,203)(119,207)(120,206)(121,205)
(122,204);
s3 := Sym(242)!(  3,  9)(  4,  8)(  5, 12)(  6, 11)(  7, 10)( 13, 14)( 15, 17)
( 18, 24)( 19, 23)( 20, 27)( 21, 26)( 22, 25)( 28, 29)( 30, 32)( 33, 39)
( 34, 38)( 35, 42)( 36, 41)( 37, 40)( 43, 44)( 45, 47)( 48, 54)( 49, 53)
( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63,114)( 64,113)( 65,117)
( 66,116)( 67,115)( 68,109)( 69,108)( 70,112)( 71,111)( 72,110)( 73,119)
( 74,118)( 75,122)( 76,121)( 77,120)( 78, 99)( 79, 98)( 80,102)( 81,101)
( 82,100)( 83, 94)( 84, 93)( 85, 97)( 86, 96)( 87, 95)( 88,104)( 89,103)
( 90,107)( 91,106)( 92,105)(123,129)(124,128)(125,132)(126,131)(127,130)
(133,134)(135,137)(138,144)(139,143)(140,147)(141,146)(142,145)(148,149)
(150,152)(153,159)(154,158)(155,162)(156,161)(157,160)(163,164)(165,167)
(168,174)(169,173)(170,177)(171,176)(172,175)(178,179)(180,182)(183,234)
(184,233)(185,237)(186,236)(187,235)(188,229)(189,228)(190,232)(191,231)
(192,230)(193,239)(194,238)(195,242)(196,241)(197,240)(198,219)(199,218)
(200,222)(201,221)(202,220)(203,214)(204,213)(205,217)(206,216)(207,215)
(208,224)(209,223)(210,227)(211,226)(212,225);
s4 := Sym(242)!(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)(  8, 68)(  9, 69)
( 10, 70)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)
( 18, 78)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 83)( 24, 84)( 25, 85)
( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 93)
( 34, 94)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 99)( 40,100)( 41,101)
( 42,102)( 43,103)( 44,104)( 45,105)( 46,106)( 47,107)( 48,108)( 49,109)
( 50,110)( 51,111)( 52,112)( 53,113)( 54,114)( 55,115)( 56,116)( 57,117)
( 58,118)( 59,119)( 60,120)( 61,121)( 62,122)(123,213)(124,214)(125,215)
(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)
(134,224)(135,225)(136,226)(137,227)(138,228)(139,229)(140,230)(141,231)
(142,232)(143,233)(144,234)(145,235)(146,236)(147,237)(148,238)(149,239)
(150,240)(151,241)(152,242)(153,183)(154,184)(155,185)(156,186)(157,187)
(158,188)(159,189)(160,190)(161,191)(162,192)(163,193)(164,194)(165,195)
(166,196)(167,197)(168,198)(169,199)(170,200)(171,201)(172,202)(173,203)
(174,204)(175,205)(176,206)(177,207)(178,208)(179,209)(180,210)(181,211)
(182,212);
poly := sub<Sym(242)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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