Polytope of Type {2,3,6,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,16}*1152
if this polytope has a name.
Group : SmallGroup(1152,133450)
Rank : 5
Schlafli Type : {2,3,6,16}
Number of vertices, edges, etc : 2, 3, 9, 48, 16
Order of s0s1s2s3s4 : 48
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 : {2,3,6,8}*576
3-fold quotients : {2,3,2,16}*384
4-fold quotients : {2,3,6,4}*288
6-fold quotients : {2,3,2,8}*192
8-fold quotients : {2,3,6,2}*144
12-fold quotients : {2,3,2,4}*96
24-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)
( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)
( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)
( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)
( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)( 89, 91)
( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)(107,109)
(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)(125,127)
(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)(143,145);;
s2 := ( 3, 7)( 4, 6)( 5, 8)( 9, 10)( 12, 16)( 13, 15)( 14, 17)( 18, 19)
( 21, 25)( 22, 24)( 23, 26)( 27, 28)( 30, 34)( 31, 33)( 32, 35)( 36, 37)
( 39, 43)( 40, 42)( 41, 44)( 45, 46)( 48, 52)( 49, 51)( 50, 53)( 54, 55)
( 57, 61)( 58, 60)( 59, 62)( 63, 64)( 66, 70)( 67, 69)( 68, 71)( 72, 73)
( 75, 79)( 76, 78)( 77, 80)( 81, 82)( 84, 88)( 85, 87)( 86, 89)( 90, 91)
( 93, 97)( 94, 96)( 95, 98)( 99,100)(102,106)(103,105)(104,107)(108,109)
(111,115)(112,114)(113,116)(117,118)(120,124)(121,123)(122,125)(126,127)
(129,133)(130,132)(131,134)(135,136)(138,142)(139,141)(140,143)(144,145);;
s3 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)
( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 39, 57)
( 40, 59)( 41, 58)( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)( 47, 64)
( 48, 66)( 49, 68)( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)( 55, 74)
( 56, 73)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)
( 82,119)( 83,118)( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)( 89,124)
( 90,126)( 91,128)( 92,127)( 93,138)( 94,140)( 95,139)( 96,141)( 97,143)
( 98,142)( 99,144)(100,146)(101,145)(102,129)(103,131)(104,130)(105,132)
(106,134)(107,133)(108,135)(109,137)(110,136);;
s4 := ( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19, 91)( 20, 92)( 21,102)( 22,103)( 23,104)( 24,105)( 25,106)( 26,107)
( 27,108)( 28,109)( 29,110)( 30, 93)( 31, 94)( 32, 95)( 33, 96)( 34, 97)
( 35, 98)( 36, 99)( 37,100)( 38,101)( 39,129)( 40,130)( 41,131)( 42,132)
( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)
( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,111)( 58,112)
( 59,113)( 60,114)( 61,115)( 62,116)( 63,117)( 64,118)( 65,119)( 66,120)
( 67,121)( 68,122)( 69,123)( 70,124)( 71,125)( 72,126)( 73,127)( 74,128);;
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*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)
( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)
( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)
( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)
( 71, 73)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)
( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)
(107,109)(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)
(125,127)(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)
(143,145);
s2 := Sym(146)!( 3, 7)( 4, 6)( 5, 8)( 9, 10)( 12, 16)( 13, 15)( 14, 17)
( 18, 19)( 21, 25)( 22, 24)( 23, 26)( 27, 28)( 30, 34)( 31, 33)( 32, 35)
( 36, 37)( 39, 43)( 40, 42)( 41, 44)( 45, 46)( 48, 52)( 49, 51)( 50, 53)
( 54, 55)( 57, 61)( 58, 60)( 59, 62)( 63, 64)( 66, 70)( 67, 69)( 68, 71)
( 72, 73)( 75, 79)( 76, 78)( 77, 80)( 81, 82)( 84, 88)( 85, 87)( 86, 89)
( 90, 91)( 93, 97)( 94, 96)( 95, 98)( 99,100)(102,106)(103,105)(104,107)
(108,109)(111,115)(112,114)(113,116)(117,118)(120,124)(121,123)(122,125)
(126,127)(129,133)(130,132)(131,134)(135,136)(138,142)(139,141)(140,143)
(144,145);
s3 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)
( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)
( 39, 57)( 40, 59)( 41, 58)( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)
( 47, 64)( 48, 66)( 49, 68)( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)
( 55, 74)( 56, 73)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)
( 81,117)( 82,119)( 83,118)( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)
( 89,124)( 90,126)( 91,128)( 92,127)( 93,138)( 94,140)( 95,139)( 96,141)
( 97,143)( 98,142)( 99,144)(100,146)(101,145)(102,129)(103,131)(104,130)
(105,132)(106,134)(107,133)(108,135)(109,137)(110,136);
s4 := Sym(146)!( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)
( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19, 91)( 20, 92)( 21,102)( 22,103)( 23,104)( 24,105)( 25,106)
( 26,107)( 27,108)( 28,109)( 29,110)( 30, 93)( 31, 94)( 32, 95)( 33, 96)
( 34, 97)( 35, 98)( 36, 99)( 37,100)( 38,101)( 39,129)( 40,130)( 41,131)
( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)
( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,111)
( 58,112)( 59,113)( 60,114)( 61,115)( 62,116)( 63,117)( 64,118)( 65,119)
( 66,120)( 67,121)( 68,122)( 69,123)( 70,124)( 71,125)( 72,126)( 73,127)
( 74,128);
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*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope