Polytope of Type {2,30,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,12}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5675)
Rank : 4
Schlafli Type : {2,30,12}
Number of vertices, edges, etc : 2, 30, 180, 12
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 : {2,30,6}*720b
   3-fold quotients : {2,10,12}*480, {2,30,4}*480a
   5-fold quotients : {2,6,12}*288a
   6-fold quotients : {2,10,6}*240, {2,30,2}*240
   9-fold quotients : {2,10,4}*160
   10-fold quotients : {2,6,6}*144a
   12-fold quotients : {2,15,2}*120
   15-fold quotients : {2,2,12}*96, {2,6,4}*96a
   18-fold quotients : {2,10,2}*80
   30-fold quotients : {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,5,2}*40
   45-fold quotients : {2,2,4}*32
   60-fold quotients : {2,2,3}*24, {2,3,2}*24
   90-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);;
s2 := (  3,  9)(  4,  8)(  5, 12)(  6, 11)(  7, 10)( 13, 14)( 15, 17)( 18, 39)
( 19, 38)( 20, 42)( 21, 41)( 22, 40)( 23, 34)( 24, 33)( 25, 37)( 26, 36)
( 27, 35)( 28, 44)( 29, 43)( 30, 47)( 31, 46)( 32, 45)( 48, 54)( 49, 53)
( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63, 84)( 64, 83)( 65, 87)
( 66, 86)( 67, 85)( 68, 79)( 69, 78)( 70, 82)( 71, 81)( 72, 80)( 73, 89)
( 74, 88)( 75, 92)( 76, 91)( 77, 90)( 93,144)( 94,143)( 95,147)( 96,146)
( 97,145)( 98,139)( 99,138)(100,142)(101,141)(102,140)(103,149)(104,148)
(105,152)(106,151)(107,150)(108,174)(109,173)(110,177)(111,176)(112,175)
(113,169)(114,168)(115,172)(116,171)(117,170)(118,179)(119,178)(120,182)
(121,181)(122,180)(123,159)(124,158)(125,162)(126,161)(127,160)(128,154)
(129,153)(130,157)(131,156)(132,155)(133,164)(134,163)(135,167)(136,166)
(137,165);;
s3 := (  3,108)(  4,109)(  5,110)(  6,111)(  7,112)(  8,113)(  9,114)( 10,115)
( 11,116)( 12,117)( 13,118)( 14,119)( 15,120)( 16,121)( 17,122)( 18, 93)
( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)( 24, 99)( 25,100)( 26,101)
( 27,102)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,123)( 34,124)
( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)( 42,132)
( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 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)( 63,138)( 64,139)( 65,140)( 66,141)
( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)( 74,149)
( 75,150)( 76,151)( 77,152)( 78,168)( 79,169)( 80,170)( 81,171)( 82,172)
( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)( 90,180)
( 91,181)( 92,182);;
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, 
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(182)!(1,2);
s1 := Sym(182)!(  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);
s2 := Sym(182)!(  3,  9)(  4,  8)(  5, 12)(  6, 11)(  7, 10)( 13, 14)( 15, 17)
( 18, 39)( 19, 38)( 20, 42)( 21, 41)( 22, 40)( 23, 34)( 24, 33)( 25, 37)
( 26, 36)( 27, 35)( 28, 44)( 29, 43)( 30, 47)( 31, 46)( 32, 45)( 48, 54)
( 49, 53)( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63, 84)( 64, 83)
( 65, 87)( 66, 86)( 67, 85)( 68, 79)( 69, 78)( 70, 82)( 71, 81)( 72, 80)
( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90)( 93,144)( 94,143)( 95,147)
( 96,146)( 97,145)( 98,139)( 99,138)(100,142)(101,141)(102,140)(103,149)
(104,148)(105,152)(106,151)(107,150)(108,174)(109,173)(110,177)(111,176)
(112,175)(113,169)(114,168)(115,172)(116,171)(117,170)(118,179)(119,178)
(120,182)(121,181)(122,180)(123,159)(124,158)(125,162)(126,161)(127,160)
(128,154)(129,153)(130,157)(131,156)(132,155)(133,164)(134,163)(135,167)
(136,166)(137,165);
s3 := Sym(182)!(  3,108)(  4,109)(  5,110)(  6,111)(  7,112)(  8,113)(  9,114)
( 10,115)( 11,116)( 12,117)( 13,118)( 14,119)( 15,120)( 16,121)( 17,122)
( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)( 24, 99)( 25,100)
( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,106)( 32,107)( 33,123)
( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)
( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 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)( 63,138)( 64,139)( 65,140)
( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)
( 74,149)( 75,150)( 76,151)( 77,152)( 78,168)( 79,169)( 80,170)( 81,171)
( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)
( 90,180)( 91,181)( 92,182);
poly := sub<Sym(182)|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, 
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