Polytope of Type {2,30,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,16}*1920
if this polytope has a name.
Group : SmallGroup(1920,203894)
Rank : 4
Schlafli Type : {2,30,16}
Number of vertices, edges, etc : 2, 30, 240, 16
Order of s₀s₁s₂s₃ : 240
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 : {2,30,8}*960
   3-fold quotients : {2,10,16}*640
   4-fold quotients : {2,30,4}*480a
   5-fold quotients : {2,6,16}*384
   6-fold quotients : {2,10,8}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {2,6,8}*192
   12-fold quotients : {2,10,4}*160
   15-fold quotients : {2,2,16}*128
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,6,4}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,2,8}*64
   40-fold quotients : {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,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)( 35, 36)
( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)
( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)( 85, 91)
( 86, 90)( 87, 89)( 94, 97)( 95, 96)( 98,103)( 99,107)(100,106)(101,105)
(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)(116,120)(117,119)
(124,127)(125,126)(128,133)(129,137)(130,136)(131,135)(132,134)(139,142)
(140,141)(143,148)(144,152)(145,151)(146,150)(147,149)(154,157)(155,156)
(158,163)(159,167)(160,166)(161,165)(162,164)(169,172)(170,171)(173,178)
(174,182)(175,181)(176,180)(177,179)(184,187)(185,186)(188,193)(189,197)
(190,196)(191,195)(192,194)(199,202)(200,201)(203,208)(204,212)(205,211)
(206,210)(207,209)(214,217)(215,216)(218,223)(219,227)(220,226)(221,225)
(222,224)(229,232)(230,231)(233,238)(234,242)(235,241)(236,240)(237,239);;
s2 := (  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, 54)( 34, 53)
( 35, 57)( 36, 56)( 37, 55)( 38, 49)( 39, 48)( 40, 52)( 41, 51)( 42, 50)
( 43, 59)( 44, 58)( 45, 62)( 46, 61)( 47, 60)( 63, 99)( 64, 98)( 65,102)
( 66,101)( 67,100)( 68, 94)( 69, 93)( 70, 97)( 71, 96)( 72, 95)( 73,104)
( 74,103)( 75,107)( 76,106)( 77,105)( 78,114)( 79,113)( 80,117)( 81,116)
( 82,115)( 83,109)( 84,108)( 85,112)( 86,111)( 87,110)( 88,119)( 89,118)
( 90,122)( 91,121)( 92,120)(123,189)(124,188)(125,192)(126,191)(127,190)
(128,184)(129,183)(130,187)(131,186)(132,185)(133,194)(134,193)(135,197)
(136,196)(137,195)(138,204)(139,203)(140,207)(141,206)(142,205)(143,199)
(144,198)(145,202)(146,201)(147,200)(148,209)(149,208)(150,212)(151,211)
(152,210)(153,234)(154,233)(155,237)(156,236)(157,235)(158,229)(159,228)
(160,232)(161,231)(162,230)(163,239)(164,238)(165,242)(166,241)(167,240)
(168,219)(169,218)(170,222)(171,221)(172,220)(173,214)(174,213)(175,217)
(176,216)(177,215)(178,224)(179,223)(180,227)(181,226)(182,225);;
s3 := (  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)(  9,129)( 10,130)
( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)
( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)
( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,168)( 34,169)
( 35,170)( 36,171)( 37,172)( 38,173)( 39,174)( 40,175)( 41,176)( 42,177)
( 43,178)( 44,179)( 45,180)( 46,181)( 47,182)( 48,153)( 49,154)( 50,155)
( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)
( 59,164)( 60,165)( 61,166)( 62,167)( 63,213)( 64,214)( 65,215)( 66,216)
( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)( 72,222)( 73,223)( 74,224)
( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)( 81,231)( 82,232)
( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)( 89,239)( 90,240)
( 91,241)( 92,242)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)( 98,188)
( 99,189)(100,190)(101,191)(102,192)(103,193)(104,194)(105,195)(106,196)
(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,203)(114,204)
(115,205)(116,206)(117,207)(118,208)(119,209)(120,210)(121,211)(122,212);;
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, 
s1*s2*s3*s2*s1*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, 
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,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)
( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)
( 85, 91)( 86, 90)( 87, 89)( 94, 97)( 95, 96)( 98,103)( 99,107)(100,106)
(101,105)(102,104)(109,112)(110,111)(113,118)(114,122)(115,121)(116,120)
(117,119)(124,127)(125,126)(128,133)(129,137)(130,136)(131,135)(132,134)
(139,142)(140,141)(143,148)(144,152)(145,151)(146,150)(147,149)(154,157)
(155,156)(158,163)(159,167)(160,166)(161,165)(162,164)(169,172)(170,171)
(173,178)(174,182)(175,181)(176,180)(177,179)(184,187)(185,186)(188,193)
(189,197)(190,196)(191,195)(192,194)(199,202)(200,201)(203,208)(204,212)
(205,211)(206,210)(207,209)(214,217)(215,216)(218,223)(219,227)(220,226)
(221,225)(222,224)(229,232)(230,231)(233,238)(234,242)(235,241)(236,240)
(237,239);
s2 := 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, 54)
( 34, 53)( 35, 57)( 36, 56)( 37, 55)( 38, 49)( 39, 48)( 40, 52)( 41, 51)
( 42, 50)( 43, 59)( 44, 58)( 45, 62)( 46, 61)( 47, 60)( 63, 99)( 64, 98)
( 65,102)( 66,101)( 67,100)( 68, 94)( 69, 93)( 70, 97)( 71, 96)( 72, 95)
( 73,104)( 74,103)( 75,107)( 76,106)( 77,105)( 78,114)( 79,113)( 80,117)
( 81,116)( 82,115)( 83,109)( 84,108)( 85,112)( 86,111)( 87,110)( 88,119)
( 89,118)( 90,122)( 91,121)( 92,120)(123,189)(124,188)(125,192)(126,191)
(127,190)(128,184)(129,183)(130,187)(131,186)(132,185)(133,194)(134,193)
(135,197)(136,196)(137,195)(138,204)(139,203)(140,207)(141,206)(142,205)
(143,199)(144,198)(145,202)(146,201)(147,200)(148,209)(149,208)(150,212)
(151,211)(152,210)(153,234)(154,233)(155,237)(156,236)(157,235)(158,229)
(159,228)(160,232)(161,231)(162,230)(163,239)(164,238)(165,242)(166,241)
(167,240)(168,219)(169,218)(170,222)(171,221)(172,220)(173,214)(174,213)
(175,217)(176,216)(177,215)(178,224)(179,223)(180,227)(181,226)(182,225);
s3 := Sym(242)!(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)(  9,129)
( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)
( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)
( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,168)
( 34,169)( 35,170)( 36,171)( 37,172)( 38,173)( 39,174)( 40,175)( 41,176)
( 42,177)( 43,178)( 44,179)( 45,180)( 46,181)( 47,182)( 48,153)( 49,154)
( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)
( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,213)( 64,214)( 65,215)
( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)( 72,222)( 73,223)
( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)( 81,231)
( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)( 89,239)
( 90,240)( 91,241)( 92,242)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)
( 98,188)( 99,189)(100,190)(101,191)(102,192)(103,193)(104,194)(105,195)
(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,203)
(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)(120,210)(121,211)
(122,212);
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, s1*s2*s3*s2*s1*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, 
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