Polytope of Type {2,48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,133451)
Rank : 4
Schlafli Type : {2,48,6}
Number of vertices, edges, etc : 2, 48, 144, 6
Order of s₀s₁s₂s₃ : 48
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 : {2,24,6}*576b
   3-fold quotients : {2,48,2}*384
   4-fold quotients : {2,12,6}*288b
   6-fold quotients : {2,24,2}*192
   8-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,16,2}*128
   12-fold quotients : {2,12,2}*96
   16-fold quotients : {2,3,6}*72
   18-fold quotients : {2,8,2}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {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, 57)( 40, 59)( 41, 58)( 42, 63)( 43, 65)( 44, 64)( 45, 60)
( 46, 62)( 47, 61)( 48, 66)( 49, 68)( 50, 67)( 51, 72)( 52, 74)( 53, 73)
( 54, 69)( 55, 71)( 56, 70)( 75,111)( 76,113)( 77,112)( 78,117)( 79,119)
( 80,118)( 81,114)( 82,116)( 83,115)( 84,120)( 85,122)( 86,121)( 87,126)
( 88,128)( 89,127)( 90,123)( 91,125)( 92,124)( 93,138)( 94,140)( 95,139)
( 96,144)( 97,146)( 98,145)( 99,141)(100,143)(101,142)(102,129)(103,131)
(104,130)(105,135)(106,137)(107,136)(108,132)(109,134)(110,133);;
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)( 39,133)( 40,132)( 41,134)( 42,130)
( 43,129)( 44,131)( 45,136)( 46,135)( 47,137)( 48,142)( 49,141)( 50,143)
( 51,139)( 52,138)( 53,140)( 54,145)( 55,144)( 56,146)( 57,115)( 58,114)
( 59,116)( 60,112)( 61,111)( 62,113)( 63,118)( 64,117)( 65,119)( 66,124)
( 67,123)( 68,125)( 69,121)( 70,120)( 71,122)( 72,127)( 73,126)( 74,128);;
s3 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)( 97, 98)
(100,101)(103,104)(106,107)(109,110)(112,113)(115,116)(118,119)(121,122)
(124,125)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143)(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*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*s3*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*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*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*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, 57)( 40, 59)( 41, 58)( 42, 63)( 43, 65)( 44, 64)
( 45, 60)( 46, 62)( 47, 61)( 48, 66)( 49, 68)( 50, 67)( 51, 72)( 52, 74)
( 53, 73)( 54, 69)( 55, 71)( 56, 70)( 75,111)( 76,113)( 77,112)( 78,117)
( 79,119)( 80,118)( 81,114)( 82,116)( 83,115)( 84,120)( 85,122)( 86,121)
( 87,126)( 88,128)( 89,127)( 90,123)( 91,125)( 92,124)( 93,138)( 94,140)
( 95,139)( 96,144)( 97,146)( 98,145)( 99,141)(100,143)(101,142)(102,129)
(103,131)(104,130)(105,135)(106,137)(107,136)(108,132)(109,134)(110,133);
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)( 39,133)( 40,132)( 41,134)
( 42,130)( 43,129)( 44,131)( 45,136)( 46,135)( 47,137)( 48,142)( 49,141)
( 50,143)( 51,139)( 52,138)( 53,140)( 54,145)( 55,144)( 56,146)( 57,115)
( 58,114)( 59,116)( 60,112)( 61,111)( 62,113)( 63,118)( 64,117)( 65,119)
( 66,124)( 67,123)( 68,125)( 69,121)( 70,120)( 71,122)( 72,127)( 73,126)
( 74,128);
s3 := Sym(146)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)
( 97, 98)(100,101)(103,104)(106,107)(109,110)(112,113)(115,116)(118,119)
(121,122)(124,125)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143)
(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*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*s3*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope