Polytope of Type {2,2,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,152556)
Rank : 5
Schlafli Type : {2,2,6,8}
Number of vertices, edges, etc : 2, 2, 18, 72, 24
Order of s0s1s2s3s4 : 8
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 : {2,2,6,4}*576
4-fold quotients : {2,2,6,4}*288
9-fold quotients : {2,2,2,8}*128
18-fold quotients : {2,2,2,4}*64
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 59)( 6, 61)( 7, 60)( 8, 65)( 9, 67)( 10, 66)( 11, 62)( 12, 64)
( 13, 63)( 14, 68)( 15, 70)( 16, 69)( 17, 74)( 18, 76)( 19, 75)( 20, 71)
( 21, 73)( 22, 72)( 23, 50)( 24, 52)( 25, 51)( 26, 56)( 27, 58)( 28, 57)
( 29, 53)( 30, 55)( 31, 54)( 32, 41)( 33, 43)( 34, 42)( 35, 47)( 36, 49)
( 37, 48)( 38, 44)( 39, 46)( 40, 45)( 77,131)( 78,133)( 79,132)( 80,137)
( 81,139)( 82,138)( 83,134)( 84,136)( 85,135)( 86,140)( 87,142)( 88,141)
( 89,146)( 90,148)( 91,147)( 92,143)( 93,145)( 94,144)( 95,122)( 96,124)
( 97,123)( 98,128)( 99,130)(100,129)(101,125)(102,127)(103,126)(104,113)
(105,115)(106,114)(107,119)(108,121)(109,120)(110,116)(111,118)(112,117);;
s3 := ( 5, 8)( 6, 9)( 7, 10)( 14, 17)( 15, 18)( 16, 19)( 23, 35)( 24, 36)
( 25, 37)( 26, 32)( 27, 33)( 28, 34)( 29, 38)( 30, 39)( 31, 40)( 41, 53)
( 42, 54)( 43, 55)( 44, 50)( 45, 51)( 46, 52)( 47, 56)( 48, 57)( 49, 58)
( 59, 62)( 60, 63)( 61, 64)( 68, 71)( 69, 72)( 70, 73)( 77, 98)( 78, 99)
( 79,100)( 80, 95)( 81, 96)( 82, 97)( 83,101)( 84,102)( 85,103)( 86,107)
( 87,108)( 88,109)( 89,104)( 90,105)( 91,106)( 92,110)( 93,111)( 94,112)
(113,143)(114,144)(115,145)(116,140)(117,141)(118,142)(119,146)(120,147)
(121,148)(122,134)(123,135)(124,136)(125,131)(126,132)(127,133)(128,137)
(129,138)(130,139);;
s4 := ( 5, 77)( 6, 80)( 7, 83)( 8, 78)( 9, 81)( 10, 84)( 11, 79)( 12, 82)
( 13, 85)( 14, 86)( 15, 89)( 16, 92)( 17, 87)( 18, 90)( 19, 93)( 20, 88)
( 21, 91)( 22, 94)( 23,104)( 24,107)( 25,110)( 26,105)( 27,108)( 28,111)
( 29,106)( 30,109)( 31,112)( 32, 95)( 33, 98)( 34,101)( 35, 96)( 36, 99)
( 37,102)( 38, 97)( 39,100)( 40,103)( 41,122)( 42,125)( 43,128)( 44,123)
( 45,126)( 46,129)( 47,124)( 48,127)( 49,130)( 50,113)( 51,116)( 52,119)
( 53,114)( 54,117)( 55,120)( 56,115)( 57,118)( 58,121)( 59,131)( 60,134)
( 61,137)( 62,132)( 63,135)( 64,138)( 65,133)( 66,136)( 67,139)( 68,140)
( 69,143)( 70,146)( 71,141)( 72,144)( 73,147)( 74,142)( 75,145)( 76,148);;
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, s1*s2*s1*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*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s2*s3*s4*s3*s4*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(148)!(1,2);
s1 := Sym(148)!(3,4);
s2 := Sym(148)!( 5, 59)( 6, 61)( 7, 60)( 8, 65)( 9, 67)( 10, 66)( 11, 62)
( 12, 64)( 13, 63)( 14, 68)( 15, 70)( 16, 69)( 17, 74)( 18, 76)( 19, 75)
( 20, 71)( 21, 73)( 22, 72)( 23, 50)( 24, 52)( 25, 51)( 26, 56)( 27, 58)
( 28, 57)( 29, 53)( 30, 55)( 31, 54)( 32, 41)( 33, 43)( 34, 42)( 35, 47)
( 36, 49)( 37, 48)( 38, 44)( 39, 46)( 40, 45)( 77,131)( 78,133)( 79,132)
( 80,137)( 81,139)( 82,138)( 83,134)( 84,136)( 85,135)( 86,140)( 87,142)
( 88,141)( 89,146)( 90,148)( 91,147)( 92,143)( 93,145)( 94,144)( 95,122)
( 96,124)( 97,123)( 98,128)( 99,130)(100,129)(101,125)(102,127)(103,126)
(104,113)(105,115)(106,114)(107,119)(108,121)(109,120)(110,116)(111,118)
(112,117);
s3 := Sym(148)!( 5, 8)( 6, 9)( 7, 10)( 14, 17)( 15, 18)( 16, 19)( 23, 35)
( 24, 36)( 25, 37)( 26, 32)( 27, 33)( 28, 34)( 29, 38)( 30, 39)( 31, 40)
( 41, 53)( 42, 54)( 43, 55)( 44, 50)( 45, 51)( 46, 52)( 47, 56)( 48, 57)
( 49, 58)( 59, 62)( 60, 63)( 61, 64)( 68, 71)( 69, 72)( 70, 73)( 77, 98)
( 78, 99)( 79,100)( 80, 95)( 81, 96)( 82, 97)( 83,101)( 84,102)( 85,103)
( 86,107)( 87,108)( 88,109)( 89,104)( 90,105)( 91,106)( 92,110)( 93,111)
( 94,112)(113,143)(114,144)(115,145)(116,140)(117,141)(118,142)(119,146)
(120,147)(121,148)(122,134)(123,135)(124,136)(125,131)(126,132)(127,133)
(128,137)(129,138)(130,139);
s4 := Sym(148)!( 5, 77)( 6, 80)( 7, 83)( 8, 78)( 9, 81)( 10, 84)( 11, 79)
( 12, 82)( 13, 85)( 14, 86)( 15, 89)( 16, 92)( 17, 87)( 18, 90)( 19, 93)
( 20, 88)( 21, 91)( 22, 94)( 23,104)( 24,107)( 25,110)( 26,105)( 27,108)
( 28,111)( 29,106)( 30,109)( 31,112)( 32, 95)( 33, 98)( 34,101)( 35, 96)
( 36, 99)( 37,102)( 38, 97)( 39,100)( 40,103)( 41,122)( 42,125)( 43,128)
( 44,123)( 45,126)( 46,129)( 47,124)( 48,127)( 49,130)( 50,113)( 51,116)
( 52,119)( 53,114)( 54,117)( 55,120)( 56,115)( 57,118)( 58,121)( 59,131)
( 60,134)( 61,137)( 62,132)( 63,135)( 64,138)( 65,133)( 66,136)( 67,139)
( 68,140)( 69,143)( 70,146)( 71,141)( 72,144)( 73,147)( 74,142)( 75,145)
( 76,148);
poly := sub<Sym(148)|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,
s1*s2*s1*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*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s2*s3*s4*s3*s4*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope