Polytope of Type {3,4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,12,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 5
Schlafli Type : {3,4,12,2}
Number of vertices, edges, etc : 6, 12, 48, 12, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,4,6,2}*576
   3-fold quotients : {3,4,4,2}*384b
   4-fold quotients : {3,2,12,2}*288
   6-fold quotients : {3,4,2,2}*192
   8-fold quotients : {3,2,6,2}*144
   12-fold quotients : {3,2,4,2}*96, {3,4,2,2}*96
   16-fold quotients : {3,2,3,2}*72
   24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  6,  7)( 10, 11)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 29)
( 18, 31)( 19, 30)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 38, 39)
( 42, 43)( 46, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 65)( 54, 67)
( 55, 66)( 56, 68)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 74, 75)( 78, 79)
( 82, 83)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,101)( 90,103)( 91,102)
( 92,104)( 93,105)( 94,107)( 95,106)( 96,108)(110,111)(114,115)(118,119)
(121,133)(122,135)(123,134)(124,136)(125,137)(126,139)(127,138)(128,140)
(129,141)(130,143)(131,142)(132,144);;
s1 := (  1, 13)(  2, 14)(  3, 16)(  4, 15)(  5, 17)(  6, 18)(  7, 20)(  8, 19)
(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 27, 28)( 31, 32)( 35, 36)( 37, 49)
( 38, 50)( 39, 52)( 40, 51)( 41, 53)( 42, 54)( 43, 56)( 44, 55)( 45, 57)
( 46, 58)( 47, 60)( 48, 59)( 63, 64)( 67, 68)( 71, 72)( 73, 85)( 74, 86)
( 75, 88)( 76, 87)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 81, 93)( 82, 94)
( 83, 96)( 84, 95)( 99,100)(103,104)(107,108)(109,121)(110,122)(111,124)
(112,123)(113,125)(114,126)(115,128)(116,127)(117,129)(118,130)(119,132)
(120,131)(135,136)(139,140)(143,144);;
s2 := (  1,  4)(  2,  3)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 13, 16)( 14, 15)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 25, 28)( 26, 27)( 29, 36)( 30, 35)
( 31, 34)( 32, 33)( 37, 40)( 38, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 45)
( 49, 52)( 50, 51)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 61, 64)( 62, 63)
( 65, 72)( 66, 71)( 67, 70)( 68, 69)( 73,112)( 74,111)( 75,110)( 76,109)
( 77,120)( 78,119)( 79,118)( 80,117)( 81,116)( 82,115)( 83,114)( 84,113)
( 85,124)( 86,123)( 87,122)( 88,121)( 89,132)( 90,131)( 91,130)( 92,129)
( 93,128)( 94,127)( 95,126)( 96,125)( 97,136)( 98,135)( 99,134)(100,133)
(101,144)(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)(108,137);;
s3 := (  1, 77)(  2, 78)(  3, 79)(  4, 80)(  5, 73)(  6, 74)(  7, 75)(  8, 76)
(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 89)( 14, 90)( 15, 91)( 16, 92)
( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25,101)( 26,102)( 27,103)( 28,104)( 29, 97)( 30, 98)( 31, 99)( 32,100)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,113)( 38,114)( 39,115)( 40,116)
( 41,109)( 42,110)( 43,111)( 44,112)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,125)( 50,126)( 51,127)( 52,128)( 53,121)( 54,122)( 55,123)( 56,124)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,137)( 62,138)( 63,139)( 64,140)
( 65,133)( 66,134)( 67,135)( 68,136)( 69,141)( 70,142)( 71,143)( 72,144);;
s4 := (145,146);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(146)!(  2,  3)(  6,  7)( 10, 11)( 13, 25)( 14, 27)( 15, 26)( 16, 28)
( 17, 29)( 18, 31)( 19, 30)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 24, 36)
( 38, 39)( 42, 43)( 46, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 65)
( 54, 67)( 55, 66)( 56, 68)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 74, 75)
( 78, 79)( 82, 83)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,101)( 90,103)
( 91,102)( 92,104)( 93,105)( 94,107)( 95,106)( 96,108)(110,111)(114,115)
(118,119)(121,133)(122,135)(123,134)(124,136)(125,137)(126,139)(127,138)
(128,140)(129,141)(130,143)(131,142)(132,144);
s1 := Sym(146)!(  1, 13)(  2, 14)(  3, 16)(  4, 15)(  5, 17)(  6, 18)(  7, 20)
(  8, 19)(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 27, 28)( 31, 32)( 35, 36)
( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 41, 53)( 42, 54)( 43, 56)( 44, 55)
( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 63, 64)( 67, 68)( 71, 72)( 73, 85)
( 74, 86)( 75, 88)( 76, 87)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 81, 93)
( 82, 94)( 83, 96)( 84, 95)( 99,100)(103,104)(107,108)(109,121)(110,122)
(111,124)(112,123)(113,125)(114,126)(115,128)(116,127)(117,129)(118,130)
(119,132)(120,131)(135,136)(139,140)(143,144);
s2 := Sym(146)!(  1,  4)(  2,  3)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 13, 16)
( 14, 15)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 25, 28)( 26, 27)( 29, 36)
( 30, 35)( 31, 34)( 32, 33)( 37, 40)( 38, 39)( 41, 48)( 42, 47)( 43, 46)
( 44, 45)( 49, 52)( 50, 51)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 61, 64)
( 62, 63)( 65, 72)( 66, 71)( 67, 70)( 68, 69)( 73,112)( 74,111)( 75,110)
( 76,109)( 77,120)( 78,119)( 79,118)( 80,117)( 81,116)( 82,115)( 83,114)
( 84,113)( 85,124)( 86,123)( 87,122)( 88,121)( 89,132)( 90,131)( 91,130)
( 92,129)( 93,128)( 94,127)( 95,126)( 96,125)( 97,136)( 98,135)( 99,134)
(100,133)(101,144)(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)
(108,137);
s3 := Sym(146)!(  1, 77)(  2, 78)(  3, 79)(  4, 80)(  5, 73)(  6, 74)(  7, 75)
(  8, 76)(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 89)( 14, 90)( 15, 91)
( 16, 92)( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25,101)( 26,102)( 27,103)( 28,104)( 29, 97)( 30, 98)( 31, 99)
( 32,100)( 33,105)( 34,106)( 35,107)( 36,108)( 37,113)( 38,114)( 39,115)
( 40,116)( 41,109)( 42,110)( 43,111)( 44,112)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,125)( 50,126)( 51,127)( 52,128)( 53,121)( 54,122)( 55,123)
( 56,124)( 57,129)( 58,130)( 59,131)( 60,132)( 61,137)( 62,138)( 63,139)
( 64,140)( 65,133)( 66,134)( 67,135)( 68,136)( 69,141)( 70,142)( 71,143)
( 72,144);
s4 := Sym(146)!(145,146);
poly := sub<Sym(146)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope