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# Polytope of Type {24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,2}*96
if this polytope has a name.
Group : SmallGroup(96,110)
Rank : 3
Schlafli Type : {24,2}
Number of vertices, edges, etc : 24, 24, 2
Order of s0s1s2 : 24
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,2,2} of size 192
{24,2,3} of size 288
{24,2,4} of size 384
{24,2,5} of size 480
{24,2,6} of size 576
{24,2,7} of size 672
{24,2,8} of size 768
{24,2,9} of size 864
{24,2,10} of size 960
{24,2,11} of size 1056
{24,2,12} of size 1152
{24,2,13} of size 1248
{24,2,14} of size 1344
{24,2,15} of size 1440
{24,2,17} of size 1632
{24,2,18} of size 1728
{24,2,19} of size 1824
{24,2,20} of size 1920
Vertex Figure Of :
{2,24,2} of size 192
{4,24,2} of size 384
{4,24,2} of size 384
{4,24,2} of size 384
{4,24,2} of size 384
{6,24,2} of size 576
{6,24,2} of size 576
{6,24,2} of size 576
{3,24,2} of size 576
{4,24,2} of size 768
{8,24,2} of size 768
{8,24,2} of size 768
{8,24,2} of size 768
{8,24,2} of size 768
{4,24,2} of size 768
{4,24,2} of size 768
{4,24,2} of size 768
{6,24,2} of size 768
{4,24,2} of size 768
{6,24,2} of size 768
{4,24,2} of size 768
{10,24,2} of size 960
{12,24,2} of size 1152
{12,24,2} of size 1152
{12,24,2} of size 1152
{4,24,2} of size 1152
{12,24,2} of size 1152
{12,24,2} of size 1152
{12,24,2} of size 1152
{4,24,2} of size 1152
{3,24,2} of size 1152
{6,24,2} of size 1152
{6,24,2} of size 1152
{6,24,2} of size 1152
{6,24,2} of size 1152
{6,24,2} of size 1152
{14,24,2} of size 1344
{18,24,2} of size 1728
{6,24,2} of size 1728
{6,24,2} of size 1728
{18,24,2} of size 1728
{6,24,2} of size 1728
{9,24,2} of size 1728
{3,24,2} of size 1728
{6,24,2} of size 1728
{6,24,2} of size 1728
{6,24,2} of size 1728
{6,24,2} of size 1728
{6,24,2} of size 1728
{20,24,2} of size 1920
{20,24,2} of size 1920
{6,24,2} of size 1920
{6,24,2} of size 1920
{10,24,2} of size 1920
{10,24,2} of size 1920
{10,24,2} of size 1920
{10,24,2} of size 1920
{4,24,2} of size 1920
{4,24,2} of size 1920
{6,24,2} of size 1920
{6,24,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,2}*48
3-fold quotients : {8,2}*32
4-fold quotients : {6,2}*24
6-fold quotients : {4,2}*16
8-fold quotients : {3,2}*12
12-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,4}*192a, {48,2}*192
3-fold covers : {72,2}*288, {24,6}*288a, {24,6}*288b
4-fold covers : {24,4}*384a, {24,8}*384a, {24,8}*384b, {48,4}*384a, {48,4}*384b, {96,2}*384, {24,4}*384c
5-fold covers : {24,10}*480, {120,2}*480
6-fold covers : {72,4}*576a, {144,2}*576, {48,6}*576a, {48,6}*576b, {24,12}*576c, {24,12}*576d
7-fold covers : {24,14}*672, {168,2}*672
8-fold covers : {24,8}*768a, {24,4}*768a, {24,8}*768d, {48,4}*768a, {48,4}*768b, {24,16}*768a, {24,16}*768b, {48,8}*768c, {48,8}*768d, {24,16}*768d, {48,8}*768e, {48,8}*768f, {24,16}*768f, {96,4}*768a, {96,4}*768b, {192,2}*768, {24,8}*768i, {24,8}*768k, {24,4}*768i, {48,4}*768c, {48,4}*768d
9-fold covers : {216,2}*864, {72,6}*864a, {72,6}*864b, {24,18}*864a, {24,6}*864a, {24,6}*864b, {24,6}*864f, {24,6}*864h
10-fold covers : {48,10}*960, {24,20}*960a, {120,4}*960a, {240,2}*960
11-fold covers : {24,22}*1056, {264,2}*1056
12-fold covers : {72,4}*1152a, {24,12}*1152a, {24,12}*1152b, {72,8}*1152b, {72,8}*1152c, {24,24}*1152b, {24,24}*1152c, {24,24}*1152e, {24,24}*1152g, {144,4}*1152a, {48,12}*1152a, {48,12}*1152b, {144,4}*1152b, {48,12}*1152d, {48,12}*1152e, {288,2}*1152, {96,6}*1152b, {96,6}*1152c, {72,4}*1152c, {24,12}*1152o, {24,12}*1152p, {24,6}*1152g, {24,6}*1152h
13-fold covers : {24,26}*1248, {312,2}*1248
14-fold covers : {48,14}*1344, {24,28}*1344a, {168,4}*1344a, {336,2}*1344
15-fold covers : {72,10}*1440, {360,2}*1440, {24,30}*1440a, {24,30}*1440b, {120,6}*1440b, {120,6}*1440c
17-fold covers : {24,34}*1632, {408,2}*1632
18-fold covers : {216,4}*1728a, {432,2}*1728, {144,6}*1728a, {144,6}*1728b, {48,18}*1728a, {48,6}*1728a, {48,6}*1728b, {72,12}*1728a, {72,12}*1728b, {24,36}*1728c, {24,12}*1728c, {24,12}*1728d, {48,6}*1728f, {24,12}*1728o, {24,4}*1728e, {24,4}*1728f, {48,6}*1728h, {24,12}*1728u
19-fold covers : {24,38}*1824, {456,2}*1824
20-fold covers : {120,4}*1920a, {24,20}*1920a, {120,8}*1920b, {120,8}*1920c, {24,40}*1920a, {24,40}*1920b, {240,4}*1920a, {48,20}*1920a, {240,4}*1920b, {48,20}*1920b, {480,2}*1920, {96,10}*1920, {24,20}*1920c, {120,4}*1920c
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)(20,21)
(23,24);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)(17,20)
(18,21)(22,24);;
s2 := (25,26);;
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, s1*s2*s1*s2,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(26)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)
(20,21)(23,24);
s1 := Sym(26)!( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)
(17,20)(18,21)(22,24);
s2 := Sym(26)!(25,26);
poly := sub<Sym(26)|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, s1*s2*s1*s2, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope