Polytope of Type {12,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1152d
if this polytope has a name.
Group : SmallGroup(1152,32543)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 24, 288, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,12}*576c
3-fold quotients : {12,8}*384b
4-fold quotients : {12,12}*288c
6-fold quotients : {12,4}*192a
8-fold quotients : {12,6}*144b, {6,12}*144c
9-fold quotients : {4,8}*128b
12-fold quotients : {12,4}*96a
16-fold quotients : {6,6}*72c
18-fold quotients : {4,4}*64
24-fold quotients : {12,2}*48, {6,4}*48a
32-fold quotients : {3,6}*36
36-fold quotients : {4,4}*32
48-fold quotients : {6,2}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)
( 45, 68)( 46, 55)( 47, 57)( 48, 56)( 49, 61)( 50, 63)( 51, 62)( 52, 58)
( 53, 60)( 54, 59)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)
( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)
(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)(114,143)
(115,139)(116,141)(117,140)(118,127)(119,129)(120,128)(121,133)(122,135)
(123,134)(124,130)(125,132)(126,131);;
s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)
( 27, 33)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)( 50, 52)
( 51, 54)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)( 61, 68)
( 62, 67)( 63, 69)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)( 78,117)
( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)( 85,125)( 86,124)
( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)( 93,138)( 94,143)
( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)(101,127)(102,129)
(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);;
s2 := ( 1, 73)( 2, 80)( 3, 78)( 4, 79)( 5, 77)( 6, 75)( 7, 76)( 8, 74)
( 9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)
( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)
( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)
( 33,102)( 34,103)( 35,101)( 36,108)( 37,136)( 38,143)( 39,141)( 40,142)
( 41,140)( 42,138)( 43,139)( 44,137)( 45,144)( 46,127)( 47,134)( 48,132)
( 49,133)( 50,131)( 51,129)( 52,130)( 53,128)( 54,135)( 55,118)( 56,125)
( 57,123)( 58,124)( 59,122)( 60,120)( 61,121)( 62,119)( 63,126)( 64,109)
( 65,116)( 66,114)( 67,115)( 68,113)( 69,111)( 70,112)( 71,110)( 72,117);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(144)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)
( 44, 69)( 45, 68)( 46, 55)( 47, 57)( 48, 56)( 49, 61)( 50, 63)( 51, 62)
( 52, 58)( 53, 60)( 54, 59)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)
(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)
(114,143)(115,139)(116,141)(117,140)(118,127)(119,129)(120,128)(121,133)
(122,135)(123,134)(124,130)(125,132)(126,131);
s1 := Sym(144)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)
( 26, 31)( 27, 33)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)
( 50, 52)( 51, 54)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)
( 61, 68)( 62, 67)( 63, 69)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)
( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)( 85,125)
( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)( 93,138)
( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)(101,127)
(102,129)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);
s2 := Sym(144)!( 1, 73)( 2, 80)( 3, 78)( 4, 79)( 5, 77)( 6, 75)( 7, 76)
( 8, 74)( 9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)
( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)
( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)
( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,136)( 38,143)( 39,141)
( 40,142)( 41,140)( 42,138)( 43,139)( 44,137)( 45,144)( 46,127)( 47,134)
( 48,132)( 49,133)( 50,131)( 51,129)( 52,130)( 53,128)( 54,135)( 55,118)
( 56,125)( 57,123)( 58,124)( 59,122)( 60,120)( 61,121)( 62,119)( 63,126)
( 64,109)( 65,116)( 66,114)( 67,115)( 68,113)( 69,111)( 70,112)( 71,110)
( 72,117);
poly := sub<Sym(144)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope