Polytope of Type {2,12,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,99274)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 24, 144, 24
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 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 : {2,12,12}*576b
3-fold quotients : {2,4,12}*384a
4-fold quotients : {2,6,12}*288b, {2,12,6}*288c
6-fold quotients : {2,4,12}*192a
8-fold quotients : {2,6,6}*144b
9-fold quotients : {2,4,4}*128
12-fold quotients : {2,2,12}*96, {2,4,6}*96a
16-fold quotients : {2,6,3}*72
18-fold quotients : {2,4,4}*64
24-fold quotients : {2,2,6}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {2,2,3}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)( 42, 51)
( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)( 59, 67)
( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)
( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)
( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)
(111,138)(112,140)(113,139)(114,141)(115,143)(116,142)(117,144)(118,146)
(119,145)(120,129)(121,131)(122,130)(123,132)(124,134)(125,133)(126,135)
(127,137)(128,136);;
s2 := ( 3, 76)( 4, 75)( 5, 77)( 6, 82)( 7, 81)( 8, 83)( 9, 79)( 10, 78)
( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)( 26,101)
( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)( 34,108)
( 35,110)( 36,106)( 37,105)( 38,107)( 39,112)( 40,111)( 41,113)( 42,118)
( 43,117)( 44,119)( 45,115)( 46,114)( 47,116)( 48,121)( 49,120)( 50,122)
( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,130)( 58,129)
( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)( 66,139)
( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)( 74,143);;
s3 := ( 3, 6)( 4, 8)( 5, 7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)
( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 36)( 28, 38)
( 29, 37)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)( 45, 54)
( 46, 56)( 47, 55)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)
( 68, 70)( 73, 74)( 75,141)( 76,143)( 77,142)( 78,138)( 79,140)( 80,139)
( 81,144)( 82,146)( 83,145)( 84,132)( 85,134)( 86,133)( 87,129)( 88,131)
( 89,130)( 90,135)( 91,137)( 92,136)( 93,114)( 94,116)( 95,115)( 96,111)
( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)(104,124)
(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*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(146)!(1,2);
s1 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)
( 42, 51)( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)
( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)
( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)
( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)
( 92,109)(111,138)(112,140)(113,139)(114,141)(115,143)(116,142)(117,144)
(118,146)(119,145)(120,129)(121,131)(122,130)(123,132)(124,134)(125,133)
(126,135)(127,137)(128,136);
s2 := Sym(146)!( 3, 76)( 4, 75)( 5, 77)( 6, 82)( 7, 81)( 8, 83)( 9, 79)
( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)
( 18, 88)( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)
( 26,101)( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)
( 34,108)( 35,110)( 36,106)( 37,105)( 38,107)( 39,112)( 40,111)( 41,113)
( 42,118)( 43,117)( 44,119)( 45,115)( 46,114)( 47,116)( 48,121)( 49,120)
( 50,122)( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,130)
( 58,129)( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)
( 66,139)( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)
( 74,143);
s3 := Sym(146)!( 3, 6)( 4, 8)( 5, 7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)
( 19, 20)( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 36)
( 28, 38)( 29, 37)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)
( 45, 54)( 46, 56)( 47, 55)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)
( 67, 71)( 68, 70)( 73, 74)( 75,141)( 76,143)( 77,142)( 78,138)( 79,140)
( 80,139)( 81,144)( 82,146)( 83,145)( 84,132)( 85,134)( 86,133)( 87,129)
( 88,131)( 89,130)( 90,135)( 91,137)( 92,136)( 93,114)( 94,116)( 95,115)
( 96,111)( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)
(104,124)(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);
poly := sub<Sym(146)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope