Polytope of Type {12,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,10}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5282)
Rank : 4
Schlafli Type : {12,6,10}
Number of vertices, edges, etc : 12, 36, 30, 10
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {6,6,10}*720c
   3-fold quotients : {12,2,10}*480
   4-fold quotients : {3,6,10}*360
   5-fold quotients : {12,6,2}*288b
   6-fold quotients : {12,2,5}*240, {6,2,10}*240
   9-fold quotients : {4,2,10}*160
   10-fold quotients : {6,6,2}*144c
   12-fold quotients : {3,2,10}*120, {6,2,5}*120
   15-fold quotients : {12,2,2}*96
   18-fold quotients : {4,2,5}*80, {2,2,10}*80
   20-fold quotients : {3,6,2}*72
   24-fold quotients : {3,2,5}*60
   30-fold quotients : {6,2,2}*48
   36-fold quotients : {2,2,5}*40
   45-fold quotients : {4,2,2}*32
   60-fold quotients : {3,2,2}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 16, 31)( 17, 32)( 18, 33)
( 19, 34)( 20, 35)( 21, 41)( 22, 42)( 23, 43)( 24, 44)( 25, 45)( 26, 36)
( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 51, 56)( 52, 57)( 53, 58)( 54, 59)
( 55, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 86)( 67, 87)
( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)
( 91,136)( 92,137)( 93,138)( 94,139)( 95,140)( 96,146)( 97,147)( 98,148)
( 99,149)(100,150)(101,141)(102,142)(103,143)(104,144)(105,145)(106,166)
(107,167)(108,168)(109,169)(110,170)(111,176)(112,177)(113,178)(114,179)
(115,180)(116,171)(117,172)(118,173)(119,174)(120,175)(121,151)(122,152)
(123,153)(124,154)(125,155)(126,161)(127,162)(128,163)(129,164)(130,165)
(131,156)(132,157)(133,158)(134,159)(135,160);;
s1 := (  1,111)(  2,112)(  3,113)(  4,114)(  5,115)(  6,106)(  7,107)(  8,108)
(  9,109)( 10,110)( 11,116)( 12,117)( 13,118)( 14,119)( 15,120)( 16, 96)
( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21, 91)( 22, 92)( 23, 93)( 24, 94)
( 25, 95)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,126)( 32,127)
( 33,128)( 34,129)( 35,130)( 36,121)( 37,122)( 38,123)( 39,124)( 40,125)
( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,156)( 47,157)( 48,158)
( 49,159)( 50,160)( 51,151)( 52,152)( 53,153)( 54,154)( 55,155)( 56,161)
( 57,162)( 58,163)( 59,164)( 60,165)( 61,141)( 62,142)( 63,143)( 64,144)
( 65,145)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,146)( 72,147)
( 73,148)( 74,149)( 75,150)( 76,171)( 77,172)( 78,173)( 79,174)( 80,175)
( 81,166)( 82,167)( 83,168)( 84,169)( 85,170)( 86,176)( 87,177)( 88,178)
( 89,179)( 90,180);;
s2 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)
( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)
(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)
(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)
(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)
(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)
(172,180)(173,179)(174,178)(175,177);;
s3 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)(118,120)
(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)
(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)
(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(180)!(  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 16, 31)( 17, 32)
( 18, 33)( 19, 34)( 20, 35)( 21, 41)( 22, 42)( 23, 43)( 24, 44)( 25, 45)
( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 51, 56)( 52, 57)( 53, 58)
( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 86)
( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)
( 75, 85)( 91,136)( 92,137)( 93,138)( 94,139)( 95,140)( 96,146)( 97,147)
( 98,148)( 99,149)(100,150)(101,141)(102,142)(103,143)(104,144)(105,145)
(106,166)(107,167)(108,168)(109,169)(110,170)(111,176)(112,177)(113,178)
(114,179)(115,180)(116,171)(117,172)(118,173)(119,174)(120,175)(121,151)
(122,152)(123,153)(124,154)(125,155)(126,161)(127,162)(128,163)(129,164)
(130,165)(131,156)(132,157)(133,158)(134,159)(135,160);
s1 := Sym(180)!(  1,111)(  2,112)(  3,113)(  4,114)(  5,115)(  6,106)(  7,107)
(  8,108)(  9,109)( 10,110)( 11,116)( 12,117)( 13,118)( 14,119)( 15,120)
( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21, 91)( 22, 92)( 23, 93)
( 24, 94)( 25, 95)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,126)
( 32,127)( 33,128)( 34,129)( 35,130)( 36,121)( 37,122)( 38,123)( 39,124)
( 40,125)( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,156)( 47,157)
( 48,158)( 49,159)( 50,160)( 51,151)( 52,152)( 53,153)( 54,154)( 55,155)
( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,141)( 62,142)( 63,143)
( 64,144)( 65,145)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,146)
( 72,147)( 73,148)( 74,149)( 75,150)( 76,171)( 77,172)( 78,173)( 79,174)
( 80,175)( 81,166)( 82,167)( 83,168)( 84,169)( 85,170)( 86,176)( 87,177)
( 88,178)( 89,179)( 90,180);
s2 := Sym(180)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)
( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)
( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)
(115,117)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)
(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)
(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)
(171,176)(172,180)(173,179)(174,178)(175,177);
s3 := Sym(180)!(  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)
( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)
( 98,100)(101,102)(103,105)(106,107)(108,110)(111,112)(113,115)(116,117)
(118,120)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)
(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)
(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)
(178,180);
poly := sub<Sym(180)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope