Questions?
See the FAQ
or other info.

# Polytope of Type {7,2,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,6,3}*1512
if this polytope has a name.
Group : SmallGroup(1512,486)
Rank : 5
Schlafli Type : {7,2,6,3}
Number of vertices, edges, etc : 7, 7, 18, 27, 9
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {7,2,6,3}*504
9-fold quotients : {7,2,2,3}*168
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (11,12)(13,14)(15,16);;
s3 := ( 9,13)(10,11)(12,14);;
s4 := ( 8, 9)(11,15)(12,16);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(16)!(2,3)(4,5)(6,7);
s1 := Sym(16)!(1,2)(3,4)(5,6);
s2 := Sym(16)!(11,12)(13,14)(15,16);
s3 := Sym(16)!( 9,13)(10,11)(12,14);
s4 := Sym(16)!( 8, 9)(11,15)(12,16);
poly := sub<Sym(16)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3 >;

```

to this polytope
{"ft_lang_label":"__label__en","ft_lang_prob":0.6966648,"math_prob":0.99552816,"size":666,"snap":"2019-35-2019-39","text_gpt3_token_len":230,"char_repetition_ratio":0.12084592,"word_repetition_ratio":0.03773585,"special_character_ratio":0.33933935,"punctuation_ratio":0.24666667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95163906,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-22T09:55:45Z\",\"WARC-Record-ID\":\"<urn:uuid:6e129461-e608-4e9e-999f-61e9ecac6b2b>\",\"Content-Length\":\"5061\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eba58544-cf1c-40e8-8ae8-4f926e6ac9f7>\",\"WARC-Concurrent-To\":\"<urn:uuid:ee5ddb24-2b9b-47bc-a133-91ff9045f82f>\",\"WARC-IP-Address\":\"209.135.140.237\",\"WARC-Target-URI\":\"http://atlas.dr-mikes-maths.com/atlas/1512/486/d7.html\",\"WARC-Payload-Digest\":\"sha1:GCPN55XHWNEUMMDLZ6THMF34DYVMLSO6\",\"WARC-Block-Digest\":\"sha1:Y7BZZVSZDBUS6WBWJKVDOJN4KQ3UGLR6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514575484.57_warc_CC-MAIN-20190922094320-20190922120320-00031.warc.gz\"}"}