Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 48, 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 : {2,6,6}*576b
   3-fold quotients : {2,12,6}*384b
   4-fold quotients : {2,3,6}*288
   6-fold quotients : {2,12,3}*192, {2,6,6}*192
   8-fold quotients : {2,6,6}*144c
   12-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,3}*48, {2,6,2}*48
   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 := (  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)( 15, 22)
( 16, 21)( 17, 26)( 18, 25)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)
( 32, 53)( 33, 58)( 34, 57)( 35, 67)( 36, 68)( 37, 72)( 38, 71)( 39, 70)
( 40, 69)( 41, 74)( 42, 73)( 43, 59)( 44, 60)( 45, 64)( 46, 63)( 47, 62)
( 48, 61)( 49, 66)( 50, 65)( 75, 76)( 77, 79)( 78, 80)( 83, 92)( 84, 91)
( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,124)(100,123)
(101,127)(102,128)(103,125)(104,126)(105,129)(106,130)(107,140)(108,139)
(109,143)(110,144)(111,141)(112,142)(113,145)(114,146)(115,132)(116,131)
(117,135)(118,136)(119,133)(120,134)(121,137)(122,138);;
s2 := (  3,107)(  4,108)(  5,110)(  6,109)(  7,113)(  8,114)(  9,111)( 10,112)
( 11, 99)( 12,100)( 13,102)( 14,101)( 15,105)( 16,106)( 17,103)( 18,104)
( 19,115)( 20,116)( 21,118)( 22,117)( 23,121)( 24,122)( 25,119)( 26,120)
( 27, 83)( 28, 84)( 29, 86)( 30, 85)( 31, 89)( 32, 90)( 33, 87)( 34, 88)
( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 81)( 40, 82)( 41, 79)( 42, 80)
( 43, 91)( 44, 92)( 45, 94)( 46, 93)( 47, 97)( 48, 98)( 49, 95)( 50, 96)
( 51,131)( 52,132)( 53,134)( 54,133)( 55,137)( 56,138)( 57,135)( 58,136)
( 59,123)( 60,124)( 61,126)( 62,125)( 63,129)( 64,130)( 65,127)( 66,128)
( 67,139)( 68,140)( 69,142)( 70,141)( 71,145)( 72,146)( 73,143)( 74,144);;
s3 := (  3, 81)(  4, 82)(  5, 77)(  6, 78)(  7, 80)(  8, 79)(  9, 75)( 10, 76)
( 11, 89)( 12, 90)( 13, 85)( 14, 86)( 15, 88)( 16, 87)( 17, 83)( 18, 84)
( 19, 97)( 20, 98)( 21, 93)( 22, 94)( 23, 96)( 24, 95)( 25, 91)( 26, 92)
( 27,129)( 28,130)( 29,125)( 30,126)( 31,128)( 32,127)( 33,123)( 34,124)
( 35,137)( 36,138)( 37,133)( 38,134)( 39,136)( 40,135)( 41,131)( 42,132)
( 43,145)( 44,146)( 45,141)( 46,142)( 47,144)( 48,143)( 49,139)( 50,140)
( 51,105)( 52,106)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 99)( 58,100)
( 59,113)( 60,114)( 61,109)( 62,110)( 63,112)( 64,111)( 65,107)( 66,108)
( 67,121)( 68,122)( 69,117)( 70,118)( 71,120)( 72,119)( 73,115)( 74,116);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope