Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 48, 144, 24, 2
Order of s₀s₁s₂s₃ : 24
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 : {6,6,2}*576b
   3-fold quotients : {12,6,2}*384b
   4-fold quotients : {3,6,2}*288
   6-fold quotients : {12,3,2}*192, {6,6,2}*192
   8-fold quotients : {6,6,2}*144c
   12-fold quotients : {3,6,2}*96, {6,3,2}*96
   16-fold quotients : {3,6,2}*72
   24-fold quotients : {3,3,2}*48, {6,2,2}*48
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope