Polytope of Type {12,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,2}*1152a
if this polytope has a name.
Group : SmallGroup(1152,99274)
Rank : 4
Schlafli Type : {12,12,2}
Number of vertices, edges, etc : 24, 144, 24, 2
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 : {12,12,2}*576a
   3-fold quotients : {4,12,2}*384a, {12,4,2}*384a
   4-fold quotients : {6,12,2}*288a, {12,6,2}*288a
   6-fold quotients : {4,12,2}*192a, {12,4,2}*192a
   8-fold quotients : {6,6,2}*144a
   9-fold quotients : {4,4,2}*128
   12-fold quotients : {2,12,2}*96, {12,2,2}*96, {4,6,2}*96a, {6,4,2}*96a
   18-fold quotients : {4,4,2}*64
   24-fold quotients : {2,6,2}*48, {6,2,2}*48
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,3,2}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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