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

Overview

Group: SmallGroup(1152,32543)
Rank: 3
Schläfli Type: {24,12}
Vertices, edges, …: 48, 288, 24
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

{8,4}*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=<(s1*s0*s1*s2)^2> of order 2

12 facets

12 of {24}*48

24 vertex figures

24 of {12}*24

Representations

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

References

None.

to this polytope.