Polytope of Type {2,2,8,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,152556)
Rank : 5
Schlafli Type : {2,2,8,6}
Number of vertices, edges, etc : 2, 2, 24, 72, 18
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 : {2,2,4,6}*576
4-fold quotients : {2,2,4,6}*288
9-fold quotients : {2,2,8,2}*128
18-fold quotients : {2,2,4,2}*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 := ( 8, 11)( 9, 12)( 10, 13)( 17, 20)( 18, 21)( 19, 22)( 23, 32)( 24, 33)
( 25, 34)( 26, 38)( 27, 39)( 28, 40)( 29, 35)( 30, 36)( 31, 37)( 41, 50)
( 42, 51)( 43, 52)( 44, 56)( 45, 57)( 46, 58)( 47, 53)( 48, 54)( 49, 55)
( 62, 65)( 63, 66)( 64, 67)( 71, 74)( 72, 75)( 73, 76)( 77, 95)( 78, 96)
( 79, 97)( 80,101)( 81,102)( 82,103)( 83, 98)( 84, 99)( 85,100)( 86,104)
( 87,105)( 88,106)( 89,110)( 90,111)( 91,112)( 92,107)( 93,108)( 94,109)
(113,140)(114,141)(115,142)(116,146)(117,147)(118,148)(119,143)(120,144)
(121,145)(122,131)(123,132)(124,133)(125,137)(126,138)(127,139)(128,134)
(129,135)(130,136);;
s3 := ( 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);;
s4 := ( 5, 60)( 6, 59)( 7, 61)( 8, 66)( 9, 65)( 10, 67)( 11, 63)( 12, 62)
( 13, 64)( 14, 69)( 15, 68)( 16, 70)( 17, 75)( 18, 74)( 19, 76)( 20, 72)
( 21, 71)( 22, 73)( 23, 51)( 24, 50)( 25, 52)( 26, 57)( 27, 56)( 28, 58)
( 29, 54)( 30, 53)( 31, 55)( 32, 42)( 33, 41)( 34, 43)( 35, 48)( 36, 47)
( 37, 49)( 38, 45)( 39, 44)( 40, 46)( 77,132)( 78,131)( 79,133)( 80,138)
( 81,137)( 82,139)( 83,135)( 84,134)( 85,136)( 86,141)( 87,140)( 88,142)
( 89,147)( 90,146)( 91,148)( 92,144)( 93,143)( 94,145)( 95,123)( 96,122)
( 97,124)( 98,129)( 99,128)(100,130)(101,126)(102,125)(103,127)(104,114)
(105,113)(106,115)(107,120)(108,119)(109,121)(110,117)(111,116)(112,118);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*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(148)!(1,2);
s1 := Sym(148)!(3,4);
s2 := Sym(148)!( 8, 11)( 9, 12)( 10, 13)( 17, 20)( 18, 21)( 19, 22)( 23, 32)
( 24, 33)( 25, 34)( 26, 38)( 27, 39)( 28, 40)( 29, 35)( 30, 36)( 31, 37)
( 41, 50)( 42, 51)( 43, 52)( 44, 56)( 45, 57)( 46, 58)( 47, 53)( 48, 54)
( 49, 55)( 62, 65)( 63, 66)( 64, 67)( 71, 74)( 72, 75)( 73, 76)( 77, 95)
( 78, 96)( 79, 97)( 80,101)( 81,102)( 82,103)( 83, 98)( 84, 99)( 85,100)
( 86,104)( 87,105)( 88,106)( 89,110)( 90,111)( 91,112)( 92,107)( 93,108)
( 94,109)(113,140)(114,141)(115,142)(116,146)(117,147)(118,148)(119,143)
(120,144)(121,145)(122,131)(123,132)(124,133)(125,137)(126,138)(127,139)
(128,134)(129,135)(130,136);
s3 := 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);
s4 := Sym(148)!( 5, 60)( 6, 59)( 7, 61)( 8, 66)( 9, 65)( 10, 67)( 11, 63)
( 12, 62)( 13, 64)( 14, 69)( 15, 68)( 16, 70)( 17, 75)( 18, 74)( 19, 76)
( 20, 72)( 21, 71)( 22, 73)( 23, 51)( 24, 50)( 25, 52)( 26, 57)( 27, 56)
( 28, 58)( 29, 54)( 30, 53)( 31, 55)( 32, 42)( 33, 41)( 34, 43)( 35, 48)
( 36, 47)( 37, 49)( 38, 45)( 39, 44)( 40, 46)( 77,132)( 78,131)( 79,133)
( 80,138)( 81,137)( 82,139)( 83,135)( 84,134)( 85,136)( 86,141)( 87,140)
( 88,142)( 89,147)( 90,146)( 91,148)( 92,144)( 93,143)( 94,145)( 95,123)
( 96,122)( 97,124)( 98,129)( 99,128)(100,130)(101,126)(102,125)(103,127)
(104,114)(105,113)(106,115)(107,120)(108,119)(109,121)(110,117)(111,116)
(112,118);
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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope