Polytope of Type {2,12,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1152c
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}*576c
3-fold quotients : {2,12,4}*384a
4-fold quotients : {2,12,6}*288b, {2,6,12}*288c
6-fold quotients : {2,12,4}*192a
8-fold quotients : {2,6,6}*144c
9-fold quotients : {2,4,4}*128
12-fold quotients : {2,12,2}*96, {2,6,4}*96a
16-fold quotients : {2,3,6}*72
18-fold quotients : {2,4,4}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {2,3,2}*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)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)
( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)( 28, 35)
( 29, 34)( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)( 45, 51)
( 46, 53)( 47, 52)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)
( 70, 74)( 71, 73)( 75,138)( 76,140)( 77,139)( 78,144)( 79,146)( 80,145)
( 81,141)( 82,143)( 83,142)( 84,129)( 85,131)( 86,130)( 87,135)( 88,137)
( 89,136)( 90,132)( 91,134)( 92,133)( 93,111)( 94,113)( 95,112)( 96,117)
( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)(104,121)
(105,126)(106,128)(107,127)(108,123)(109,125)(110,124);;
s2 := ( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)( 10, 81)
( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)
( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)( 26, 95)
( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)( 34,102)
( 35,104)( 36,109)( 37,108)( 38,110)( 39,115)( 40,114)( 41,116)( 42,112)
( 43,111)( 44,113)( 45,118)( 46,117)( 47,119)( 48,124)( 49,123)( 50,125)
( 51,121)( 52,120)( 53,122)( 54,127)( 55,126)( 56,128)( 57,133)( 58,132)
( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)( 66,142)
( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)( 74,146);;
s3 := ( 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);;
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*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*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 ];;
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)( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)
( 28, 35)( 29, 34)( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)
( 45, 51)( 46, 53)( 47, 52)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)
( 69, 72)( 70, 74)( 71, 73)( 75,138)( 76,140)( 77,139)( 78,144)( 79,146)
( 80,145)( 81,141)( 82,143)( 83,142)( 84,129)( 85,131)( 86,130)( 87,135)
( 88,137)( 89,136)( 90,132)( 91,134)( 92,133)( 93,111)( 94,113)( 95,112)
( 96,117)( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)
(104,121)(105,126)(106,128)(107,127)(108,123)(109,125)(110,124);
s2 := Sym(146)!( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)
( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)
( 18, 91)( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)
( 26, 95)( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)
( 34,102)( 35,104)( 36,109)( 37,108)( 38,110)( 39,115)( 40,114)( 41,116)
( 42,112)( 43,111)( 44,113)( 45,118)( 46,117)( 47,119)( 48,124)( 49,123)
( 50,125)( 51,121)( 52,120)( 53,122)( 54,127)( 55,126)( 56,128)( 57,133)
( 58,132)( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)
( 66,142)( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)
( 74,146);
s3 := 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);
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*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*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 >;
to this polytope