Questions?
See the FAQ
or other info.

# Polytope of Type {32}

Atlas Canonical Name : {32}*64
Also Known As : 32-gon, {32}. if this polytope has another name.
Group : SmallGroup(64,52)
Rank : 2
Schlafli Type : {32}
Number of vertices, edges, etc : 32, 32
Order of s0s1 : 32
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{32,2} of size 128
{32,4} of size 256
{32,4} of size 256
{32,6} of size 384
{32,4} of size 512
{32,4} of size 512
{32,8} of size 512
{32,8} of size 512
{32,8} of size 512
{32,8} of size 512
{32,10} of size 640
{32,12} of size 768
{32,12} of size 768
{32,14} of size 896
{32,18} of size 1152
{32,6} of size 1152
{32,20} of size 1280
{32,20} of size 1280
{32,22} of size 1408
{32,26} of size 1664
{32,28} of size 1792
{32,28} of size 1792
{32,30} of size 1920
Vertex Figure Of :
{2,32} of size 128
{4,32} of size 256
{4,32} of size 256
{6,32} of size 384
{4,32} of size 512
{4,32} of size 512
{8,32} of size 512
{8,32} of size 512
{8,32} of size 512
{8,32} of size 512
{10,32} of size 640
{12,32} of size 768
{12,32} of size 768
{14,32} of size 896
{18,32} of size 1152
{6,32} of size 1152
{20,32} of size 1280
{20,32} of size 1280
{22,32} of size 1408
{26,32} of size 1664
{28,32} of size 1792
{28,32} of size 1792
{30,32} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {16}*32
4-fold quotients : {8}*16
8-fold quotients : {4}*8
16-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {64}*128
3-fold covers : {96}*192
4-fold covers : {128}*256
5-fold covers : {160}*320
6-fold covers : {192}*384
7-fold covers : {224}*448
8-fold covers : {256}*512
9-fold covers : {288}*576
10-fold covers : {320}*640
11-fold covers : {352}*704
12-fold covers : {384}*768
13-fold covers : {416}*832
14-fold covers : {448}*896
15-fold covers : {480}*960
17-fold covers : {544}*1088
18-fold covers : {576}*1152
19-fold covers : {608}*1216
20-fold covers : {640}*1280
21-fold covers : {672}*1344
22-fold covers : {704}*1408
23-fold covers : {736}*1472
25-fold covers : {800}*1600
26-fold covers : {832}*1664
27-fold covers : {864}*1728
28-fold covers : {896}*1792
29-fold covers : {928}*1856
30-fold covers : {960}*1920
31-fold covers : {992}*1984
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);;
poly := Group([s0,s1]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;
rels := [ s0*s0, s1*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*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(32)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31);
s1 := Sym(32)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);
poly := sub<Sym(32)|s0,s1>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope