Polytope of Type {12,24} with group SmallGroup(1152,32543)

Overview

Group: SmallGroup(1152,32543)
Rank: 3
Schläfli Type: {12,24}
Vertices, edges, …: 24, 288, 48
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{12,12}*576a

3-fold

4-fold

{12,12}*288a

6-fold

8-fold

9-fold

{4,8}*128b

12-fold

16-fold

{6,6}*72a

18-fold

{4,4}*64

24-fold

36-fold

{4,4}*32

48-fold

72-fold

96-fold

144-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1*s2*s1)^2> of order 2

24 facets

24 of {12}*24

12 vertex figures

12 of {24}*48

Representations

Permutation Representation (GAP)

s0 := (  1, 73)(  2, 78)(  3, 80)(  4, 76)(  5, 81)(  6, 74)(  7, 79)(  8, 75)(  9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)( 16, 88)( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)( 24, 92)( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)( 32,108)( 33,101)( 34,106)( 35,102)( 36,104)( 37,109)( 38,114)( 39,116)( 40,112)( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)( 48,125)( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)( 56,132)( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)( 64,136)( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)( 72,140);;
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, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*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, 
s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(144)!(  1, 73)(  2, 78)(  3, 80)(  4, 76)(  5, 81)(  6, 74)(  7, 79)(  8, 75)(  9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)( 16, 88)( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)( 24, 92)( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)( 32,108)( 33,101)( 34,106)( 35,102)( 36,104)( 37,109)( 38,114)( 39,116)( 40,112)( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)( 48,125)( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)( 56,132)( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)( 64,136)( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)( 72,140);
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, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*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, 
s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;

References

None.

to this polytope.