Polytope of Type {2,8,3,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,3,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {2,8,3,6}
Number of vertices, edges, etc : 2, 16, 24, 18, 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 : {2,4,3,6}*576
3-fold quotients : {2,8,3,2}*384
4-fold quotients : {2,4,3,6}*288
6-fold quotients : {2,4,3,2}*192
8-fold quotients : {2,2,3,6}*144
12-fold quotients : {2,4,3,2}*96
24-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 79)( 4, 80)( 5, 82)( 6, 81)( 7, 76)( 8, 75)( 9, 77)( 10, 78)
( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 84)( 16, 83)( 17, 85)( 18, 86)
( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)( 26, 94)
( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)( 34,102)
( 35,111)( 36,112)( 37,114)( 38,113)( 39,108)( 40,107)( 41,109)( 42,110)
( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)( 50,118)
( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)( 58,126)
( 59,135)( 60,136)( 61,138)( 62,137)( 63,132)( 64,131)( 65,133)( 66,134)
( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)( 74,142);;
s2 := ( 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);;
s3 := ( 3, 59)( 4, 60)( 5, 65)( 6, 66)( 7, 64)( 8, 63)( 9, 61)( 10, 62)
( 11, 51)( 12, 52)( 13, 57)( 14, 58)( 15, 56)( 16, 55)( 17, 53)( 18, 54)
( 19, 67)( 20, 68)( 21, 73)( 22, 74)( 23, 72)( 24, 71)( 25, 69)( 26, 70)
( 27, 35)( 28, 36)( 29, 41)( 30, 42)( 31, 40)( 32, 39)( 33, 37)( 34, 38)
( 45, 49)( 46, 50)( 47, 48)( 75,132)( 76,131)( 77,138)( 78,137)( 79,135)
( 80,136)( 81,134)( 82,133)( 83,124)( 84,123)( 85,130)( 86,129)( 87,127)
( 88,128)( 89,126)( 90,125)( 91,140)( 92,139)( 93,146)( 94,145)( 95,143)
( 96,144)( 97,142)( 98,141)( 99,108)(100,107)(101,114)(102,113)(103,111)
(104,112)(105,110)(106,109)(115,116)(117,122)(118,121);;
s4 := ( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 17, 25)( 18, 26)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)( 66, 74)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(113,121)(114,122)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146);;
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*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,
s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*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)!( 3, 79)( 4, 80)( 5, 82)( 6, 81)( 7, 76)( 8, 75)( 9, 77)
( 10, 78)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 84)( 16, 83)( 17, 85)
( 18, 86)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)
( 26, 94)( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)
( 34,102)( 35,111)( 36,112)( 37,114)( 38,113)( 39,108)( 40,107)( 41,109)
( 42,110)( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)
( 50,118)( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)
( 58,126)( 59,135)( 60,136)( 61,138)( 62,137)( 63,132)( 64,131)( 65,133)
( 66,134)( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)
( 74,142);
s2 := 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);
s3 := Sym(146)!( 3, 59)( 4, 60)( 5, 65)( 6, 66)( 7, 64)( 8, 63)( 9, 61)
( 10, 62)( 11, 51)( 12, 52)( 13, 57)( 14, 58)( 15, 56)( 16, 55)( 17, 53)
( 18, 54)( 19, 67)( 20, 68)( 21, 73)( 22, 74)( 23, 72)( 24, 71)( 25, 69)
( 26, 70)( 27, 35)( 28, 36)( 29, 41)( 30, 42)( 31, 40)( 32, 39)( 33, 37)
( 34, 38)( 45, 49)( 46, 50)( 47, 48)( 75,132)( 76,131)( 77,138)( 78,137)
( 79,135)( 80,136)( 81,134)( 82,133)( 83,124)( 84,123)( 85,130)( 86,129)
( 87,127)( 88,128)( 89,126)( 90,125)( 91,140)( 92,139)( 93,146)( 94,145)
( 95,143)( 96,144)( 97,142)( 98,141)( 99,108)(100,107)(101,114)(102,113)
(103,111)(104,112)(105,110)(106,109)(115,116)(117,122)(118,121);
s4 := Sym(146)!( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 17, 25)
( 18, 26)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)
( 66, 74)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(113,121)
(114,122)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146);
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*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, s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope