Polytope of Type {6,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,6}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157621)
Rank : 4
Schlafli Type : {6,8,6}
Number of vertices, edges, etc : 12, 48, 48, 6
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {6,4,6}*576b
   3-fold quotients : {6,8,2}*384c
   4-fold quotients : {3,4,6}*288
   6-fold quotients : {6,4,2}*192
   8-fold quotients : {6,2,6}*144
   12-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   24-fold quotients : {3,4,2}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   48-fold quotients : {2,2,3}*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 := (  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)
( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)
( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)
( 48, 70)( 73, 74)( 77, 80)( 78, 79)( 81, 82)( 85, 88)( 86, 87)( 89, 90)
( 93, 96)( 94, 95)( 97,122)( 98,121)( 99,123)(100,124)(101,128)(102,127)
(103,126)(104,125)(105,130)(106,129)(107,131)(108,132)(109,136)(110,135)
(111,134)(112,133)(113,138)(114,137)(115,139)(116,140)(117,144)(118,143)
(119,142)(120,141);;
s1 := (  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)(  8, 28)
(  9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)( 16, 36)
( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)
( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)( 68, 72)
( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)( 79, 99)
( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)
( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)( 95,115)
( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)(139,143)
(140,144)(141,142);;
s2 := (  1, 75)(  2, 76)(  3, 74)(  4, 73)(  5, 79)(  6, 80)(  7, 78)(  8, 77)
(  9, 91)( 10, 92)( 11, 90)( 12, 89)( 13, 95)( 14, 96)( 15, 94)( 16, 93)
( 17, 83)( 18, 84)( 19, 82)( 20, 81)( 21, 87)( 22, 88)( 23, 86)( 24, 85)
( 25, 99)( 26,100)( 27, 98)( 28, 97)( 29,103)( 30,104)( 31,102)( 32,101)
( 33,115)( 34,116)( 35,114)( 36,113)( 37,119)( 38,120)( 39,118)( 40,117)
( 41,107)( 42,108)( 43,106)( 44,105)( 45,111)( 46,112)( 47,110)( 48,109)
( 49,123)( 50,124)( 51,122)( 52,121)( 53,127)( 54,128)( 55,126)( 56,125)
( 57,139)( 58,140)( 59,138)( 60,137)( 61,143)( 62,144)( 63,142)( 64,141)
( 65,131)( 66,132)( 67,130)( 68,129)( 69,135)( 70,136)( 71,134)( 72,133);;
s3 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)
( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)( 80, 88)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope