Polytope of Type {2,12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,24}*1152f
if this polytope has a name.
Group : SmallGroup(1152,98805)
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}*576c
   3-fold quotients : {2,12,8}*384b
   4-fold quotients : {2,12,6}*288b, {2,6,12}*288c
   6-fold quotients : {2,12,4}*192a
   8-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,4,8}*128b
   12-fold quotients : {2,12,2}*96, {2,6,4}*96a
   16-fold quotients : {2,3,6}*72
   18-fold quotients : {2,4,4}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {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 := (  4,  5)(  6,  9)(  7, 11)(  8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)( 28, 35)( 29, 34)( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)( 45, 51)( 46, 53)( 47, 52)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 75,129)( 76,131)( 77,130)( 78,135)( 79,137)( 80,136)( 81,132)( 82,134)( 83,133)( 84,138)( 85,140)( 86,139)( 87,144)( 88,146)( 89,145)( 90,141)( 91,143)( 92,142)( 93,111)( 94,113)( 95,112)( 96,117)( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)(104,121)(105,126)(106,128)(107,127)(108,123)(109,125)(110,124);;
s2 := (  3, 79)(  4, 78)(  5, 80)(  6, 76)(  7, 75)(  8, 77)(  9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)( 26,104)( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)( 34, 93)( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,124)( 40,123)( 41,125)( 42,121)( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)( 50,116)( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,133)( 58,132)( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)( 66,142)( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)( 74,146);;
s3 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)(127,146)(128,145);;
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*s3*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope