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Polytope of Type {2,3,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,8,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {2,3,8,6}
Number of vertices, edges, etc : 2, 6, 24, 48, 6
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 : {2,3,4,6}*576
   3-fold quotients : {2,3,8,2}*384
   6-fold quotients : {2,3,4,2}*192
   8-fold quotients : {2,3,2,6}*144
   12-fold quotients : {2,3,4,2}*96
   16-fold quotients : {2,3,2,3}*72
   24-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  5,  8)(  6,  7)(  9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)
( 25, 26)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)( 32, 53)( 33, 58)
( 34, 57)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 66)
( 42, 65)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 74)
( 50, 73)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)
( 93, 95)( 94, 96)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)
(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)
(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)
(121,145)(122,146);;
s2 := (  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 33)(  8, 34)(  9, 31)( 10, 32)
( 11, 35)( 12, 36)( 13, 38)( 14, 37)( 15, 41)( 16, 42)( 17, 39)( 18, 40)
( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 49)( 24, 50)( 25, 47)( 26, 48)
( 53, 54)( 55, 57)( 56, 58)( 61, 62)( 63, 65)( 64, 66)( 69, 70)( 71, 73)
( 72, 74)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)( 80,105)( 81,104)
( 82,103)( 83,108)( 84,107)( 85,109)( 86,110)( 87,114)( 88,113)( 89,112)
( 90,111)( 91,116)( 92,115)( 93,117)( 94,118)( 95,122)( 96,121)( 97,120)
( 98,119)(123,124)(127,130)(128,129)(131,132)(135,138)(136,137)(139,140)
(143,146)(144,145);;
s3 := (  3, 81)(  4, 82)(  5, 79)(  6, 80)(  7, 78)(  8, 77)(  9, 76)( 10, 75)
( 11, 97)( 12, 98)( 13, 95)( 14, 96)( 15, 94)( 16, 93)( 17, 92)( 18, 91)
( 19, 89)( 20, 90)( 21, 87)( 22, 88)( 23, 86)( 24, 85)( 25, 84)( 26, 83)
( 27,105)( 28,106)( 29,103)( 30,104)( 31,102)( 32,101)( 33,100)( 34, 99)
( 35,121)( 36,122)( 37,119)( 38,120)( 39,118)( 40,117)( 41,116)( 42,115)
( 43,113)( 44,114)( 45,111)( 46,112)( 47,110)( 48,109)( 49,108)( 50,107)
( 51,129)( 52,130)( 53,127)( 54,128)( 55,126)( 56,125)( 57,124)( 58,123)
( 59,145)( 60,146)( 61,143)( 62,144)( 63,142)( 64,141)( 65,140)( 66,139)
( 67,137)( 68,138)( 69,135)( 70,136)( 71,134)( 72,133)( 73,132)( 74,131);;
s4 := (  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)(  9, 17)( 10, 18)
( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)( 33, 41)( 34, 42)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)( 80, 88)( 81, 89)( 82, 90)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(129,137)(130,138);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  5,  8)(  6,  7)(  9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)
( 22, 23)( 25, 26)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)( 32, 53)
( 33, 58)( 34, 57)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)
( 41, 66)( 42, 65)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 69)
( 49, 74)( 50, 73)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)
( 91, 92)( 93, 95)( 94, 96)( 99,124)(100,123)(101,127)(102,128)(103,125)
(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)
(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)
(120,142)(121,145)(122,146);
s2 := Sym(146)!(  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 33)(  8, 34)(  9, 31)
( 10, 32)( 11, 35)( 12, 36)( 13, 38)( 14, 37)( 15, 41)( 16, 42)( 17, 39)
( 18, 40)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 49)( 24, 50)( 25, 47)
( 26, 48)( 53, 54)( 55, 57)( 56, 58)( 61, 62)( 63, 65)( 64, 66)( 69, 70)
( 71, 73)( 72, 74)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)( 80,105)
( 81,104)( 82,103)( 83,108)( 84,107)( 85,109)( 86,110)( 87,114)( 88,113)
( 89,112)( 90,111)( 91,116)( 92,115)( 93,117)( 94,118)( 95,122)( 96,121)
( 97,120)( 98,119)(123,124)(127,130)(128,129)(131,132)(135,138)(136,137)
(139,140)(143,146)(144,145);
s3 := Sym(146)!(  3, 81)(  4, 82)(  5, 79)(  6, 80)(  7, 78)(  8, 77)(  9, 76)
( 10, 75)( 11, 97)( 12, 98)( 13, 95)( 14, 96)( 15, 94)( 16, 93)( 17, 92)
( 18, 91)( 19, 89)( 20, 90)( 21, 87)( 22, 88)( 23, 86)( 24, 85)( 25, 84)
( 26, 83)( 27,105)( 28,106)( 29,103)( 30,104)( 31,102)( 32,101)( 33,100)
( 34, 99)( 35,121)( 36,122)( 37,119)( 38,120)( 39,118)( 40,117)( 41,116)
( 42,115)( 43,113)( 44,114)( 45,111)( 46,112)( 47,110)( 48,109)( 49,108)
( 50,107)( 51,129)( 52,130)( 53,127)( 54,128)( 55,126)( 56,125)( 57,124)
( 58,123)( 59,145)( 60,146)( 61,143)( 62,144)( 63,142)( 64,141)( 65,140)
( 66,139)( 67,137)( 68,138)( 69,135)( 70,136)( 71,134)( 72,133)( 73,132)
( 74,131);
s4 := Sym(146)!(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)(  9, 17)
( 10, 18)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)( 33, 41)
( 34, 42)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)( 80, 88)( 81, 89)
( 82, 90)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(129,137)
(130,138);
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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >; 
 

to this polytope