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