Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1152f
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 24, 144, 24
Order of s₀s₁s₂s₃ : 12
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 : {2,12,6}*576a
   3-fold quotients : {2,4,12}*384b
   4-fold quotients : {2,6,12}*288a, {2,12,6}*288d
   6-fold quotients : {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   8-fold quotients : {2,6,6}*144a
   12-fold quotients : {2,2,12}*96, {2,6,4}*96a, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   24-fold quotients : {2,4,3}*48, {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,3}*24, {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7, 13)(  8, 14)(  9, 11)( 10, 12)( 15, 17)( 16, 18)
( 19, 25)( 20, 26)( 21, 23)( 22, 24)( 27, 29)( 28, 30)( 31, 37)( 32, 38)
( 33, 35)( 34, 36)( 39, 41)( 40, 42)( 43, 49)( 44, 50)( 45, 47)( 46, 48)
( 51, 53)( 52, 54)( 55, 61)( 56, 62)( 57, 59)( 58, 60)( 63, 65)( 64, 66)
( 67, 73)( 68, 74)( 69, 71)( 70, 72)( 75, 77)( 76, 78)( 79, 85)( 80, 86)
( 81, 83)( 82, 84)( 87, 89)( 88, 90)( 91, 97)( 92, 98)( 93, 95)( 94, 96)
( 99,101)(100,102)(103,109)(104,110)(105,107)(106,108)(111,113)(112,114)
(115,121)(116,122)(117,119)(118,120)(123,125)(124,126)(127,133)(128,134)
(129,131)(130,132)(135,137)(136,138)(139,145)(140,146)(141,143)(142,144);;
s2 := (  3,  7)(  4,  9)(  5,  8)(  6, 10)( 12, 13)( 15, 31)( 16, 33)( 17, 32)
( 18, 34)( 19, 27)( 20, 29)( 21, 28)( 22, 30)( 23, 35)( 24, 37)( 25, 36)
( 26, 38)( 39, 43)( 40, 45)( 41, 44)( 42, 46)( 48, 49)( 51, 67)( 52, 69)
( 53, 68)( 54, 70)( 55, 63)( 56, 65)( 57, 64)( 58, 66)( 59, 71)( 60, 73)
( 61, 72)( 62, 74)( 75,115)( 76,117)( 77,116)( 78,118)( 79,111)( 80,113)
( 81,112)( 82,114)( 83,119)( 84,121)( 85,120)( 86,122)( 87,139)( 88,141)
( 89,140)( 90,142)( 91,135)( 92,137)( 93,136)( 94,138)( 95,143)( 96,145)
( 97,144)( 98,146)( 99,127)(100,129)(101,128)(102,130)(103,123)(104,125)
(105,124)(106,126)(107,131)(108,133)(109,132)(110,134);;
s3 := (  3, 99)(  4,102)(  5,101)(  6,100)(  7,103)(  8,106)(  9,105)( 10,104)
( 11,107)( 12,110)( 13,109)( 14,108)( 15, 87)( 16, 90)( 17, 89)( 18, 88)
( 19, 91)( 20, 94)( 21, 93)( 22, 92)( 23, 95)( 24, 98)( 25, 97)( 26, 96)
( 27, 75)( 28, 78)( 29, 77)( 30, 76)( 31, 79)( 32, 82)( 33, 81)( 34, 80)
( 35, 83)( 36, 86)( 37, 85)( 38, 84)( 39,135)( 40,138)( 41,137)( 42,136)
( 43,139)( 44,142)( 45,141)( 46,140)( 47,143)( 48,146)( 49,145)( 50,144)
( 51,123)( 52,126)( 53,125)( 54,124)( 55,127)( 56,130)( 57,129)( 58,128)
( 59,131)( 60,134)( 61,133)( 62,132)( 63,111)( 64,114)( 65,113)( 66,112)
( 67,115)( 68,118)( 69,117)( 70,116)( 71,119)( 72,122)( 73,121)( 74,120);;
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope