Polytope of Type {2,12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,24}*1152d
if this polytope has a name.
Group : SmallGroup(1152,98801)
Rank : 4
Schlafli Type : {2,12,24}
Number of vertices, edges, etc : 2, 12, 144, 24
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 : {2,12,12}*576a
   3-fold quotients : {2,4,24}*384b, {2,12,8}*384b
   4-fold quotients : {2,6,12}*288a, {2,12,6}*288a
   6-fold quotients : {2,4,12}*192a, {2,12,4}*192a
   8-fold quotients : {2,6,6}*144a
   9-fold quotients : {2,4,8}*128b
   12-fold quotients : {2,2,12}*96, {2,12,2}*96, {2,4,6}*96a, {2,6,4}*96a
   18-fold quotients : {2,4,4}*64
   24-fold quotients : {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*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 := (  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 21, 30)( 22, 31)
( 23, 32)( 24, 36)( 25, 37)( 26, 38)( 27, 33)( 28, 34)( 29, 35)( 42, 45)
( 43, 46)( 44, 47)( 51, 54)( 52, 55)( 53, 56)( 57, 66)( 58, 67)( 59, 68)
( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75,111)( 76,112)
( 77,113)( 78,117)( 79,118)( 80,119)( 81,114)( 82,115)( 83,116)( 84,120)
( 85,121)( 86,122)( 87,126)( 88,127)( 89,128)( 90,123)( 91,124)( 92,125)
( 93,138)( 94,139)( 95,140)( 96,144)( 97,145)( 98,146)( 99,141)(100,142)
(101,143)(102,129)(103,130)(104,131)(105,135)(106,136)(107,137)(108,132)
(109,133)(110,134);;
s2 := (  3, 78)(  4, 80)(  5, 79)(  6, 75)(  7, 77)(  8, 76)(  9, 81)( 10, 83)
( 11, 82)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)( 18, 90)
( 19, 92)( 20, 91)( 21,105)( 22,107)( 23,106)( 24,102)( 25,104)( 26,103)
( 27,108)( 28,110)( 29,109)( 30, 96)( 31, 98)( 32, 97)( 33, 93)( 34, 95)
( 35, 94)( 36, 99)( 37,101)( 38,100)( 39,114)( 40,116)( 41,115)( 42,111)
( 43,113)( 44,112)( 45,117)( 46,119)( 47,118)( 48,123)( 49,125)( 50,124)
( 51,120)( 52,122)( 53,121)( 54,126)( 55,128)( 56,127)( 57,141)( 58,143)
( 59,142)( 60,138)( 61,140)( 62,139)( 63,144)( 64,146)( 65,145)( 66,132)
( 67,134)( 68,133)( 69,129)( 70,131)( 71,130)( 72,135)( 73,137)( 74,136);;
s3 := (  3,  4)(  6,  7)(  9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 31)( 22, 30)
( 23, 32)( 24, 34)( 25, 33)( 26, 35)( 27, 37)( 28, 36)( 29, 38)( 39, 49)
( 40, 48)( 41, 50)( 42, 52)( 43, 51)( 44, 53)( 45, 55)( 46, 54)( 47, 56)
( 57, 58)( 60, 61)( 63, 64)( 66, 67)( 69, 70)( 72, 73)( 75, 94)( 76, 93)
( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81,100)( 82, 99)( 83,101)( 84,103)
( 85,102)( 86,104)( 87,106)( 88,105)( 89,107)( 90,109)( 91,108)( 92,110)
(111,139)(112,138)(113,140)(114,142)(115,141)(116,143)(117,145)(118,144)
(119,146)(120,130)(121,129)(122,131)(123,133)(124,132)(125,134)(126,136)
(127,135)(128,137);;
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*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*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, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope