Acronym teddot
Name tetradiminished dodecateron,
bidrap alterprism,
bidrap atop gyroinverted bidrap
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art 
                   N                
                M                   
                                    
              Q      P              
                                    
                                    
                                    
                                    
                                    
    *                          f    
                                    
  D     C                    *     c
A     B                    a     *  
                                    
    *                          e    
                                    
                                    
                                    
                                    
                                    
              p      q              
                                    
                   m                
                n
Face vector 16, 54, 78, 54, 16
Confer
segmentotera:
triddippy  
uniform relative:
dot  
External
links 		polytopewiki

That equatorial ope of dot allows for a (there mentioned) tetra-diminishing: that is, the antiparallelly aligned raps from the lace city of dot could be bidiminished each into bidraps, however thereby aligning the omissions at the pair of octs (of that diametral ope) orthogonally. Thus that pair of opposite bidraps not truely is an mutually inverted pair, it rather is also gyrated into an alternate positioning wrt. that chosen oct-axes. Although that tetra-diminishing of ope itself yielded free q-edges, its usage in dot will result in this true CRF.

By consideration of the below incidence matrix it moreover becomes obvious that it is (at least abstractly) selfdual too.

The 4 individual diminishings do chop off a triddippy each.

Within the labelling of the above lace city starts with dot within its representation as rap || -rap, and each rap in turn as tet || oct. It labels the vertices of the right oct by ABCDEF, those of the left one by abcdef in a mutually parallel way. It further labels those of the top tet by MNPQ and that of the dual bottom tet by mnpq in the mutually inverted way. Diminishing takes place in the first oct by omission of E nad F, while in the second oct b and d gets omitted, thus leaving the squares ABCD and aecf respectively. Further we have AB || CD || PQ || pq, AD || BC || MN || mn, ae || cf || MP || mp, af || ce || NQ || nq quite obviously. Note first that the vertices B, D, e, f in turn have for their hull a second ope-inscribed q-tet; those 4 vertices form the special vertex class to be separated. Note furthermore that there are just 6 edges, which are not parallelly aligned to any of those 2 remainder square's sides; those are Aa, Cc, MQ, NP, mq, np.


Incidence matrix

12 * | 1  4  2 |  6  4  6 1 | 2  8  8 |  6 2
 * 4 | 0  0  6 |  0  6  6 3 | 0  6 12 |  6 3  B, D, e, f
-----+---------+------------+---------+-----
 2 0 | 6  *  * |  4  0  0 0 | 2  4  0 |  4 0  Aa, Cc, MQ, NP, mq, np
 2 0 | * 24  * |  2  1  2 0 | 1  4  3 |  4 1
 1 1 | *  * 24 |  0  2  2 1 | 0  3  6 |  4 2
-----+---------+------------+---------+-----
 3 0 | 1  2  0 | 24  *  * * | 1  2  0 |  3 0
 2 1 | 0  1  2 |  * 24  * * | 0  2  2 |  3 1
 3 1 | 0  2  2 |  *  * 24 * | 0  1  2 |  2 1
 2 2 | 0  0  4 |  *  *  * 6 | 0  0  4 |  2 2
-----+---------+------------+---------+-----
 4 0 | 2  4  0 |  4  0  0 0 | 6  *  * |  2 0  tet
 4 1 | 1  4  3 |  2  2  1 0 | * 24  * |  2 0  squippy
 4 2 | 0  3  6 |  0  2  2 1 | *  * 24 |  1 1  trip
-----+---------+------------+---------+-----
 6 2 | 2  8  8 |  6  6  4 1 | 1  4  2 | 12 *  bidrap
 6 3 | 0  6 12 |  0  6  6 3 | 0  0  6 |  * 4  triddip


tet || (pseudo) 4-dim ope || dual tet

4 * * * | 2 1 2 2 0 0 0 0 0 0 | 3 4 2 2 1 2 2 1 0 0 0 0 0 0 0 | 1 1 6 2 4 2 2 0 0 0 0 | 2 3 2 1 0  M,N,P,Q
* 4 * * | 0 0 2 0 1 2 2 0 0 0 | 0 2 1 0 2 2 2 0 1 2 2 2 1 0 0 | 0 1 2 2 2 4 2 2 1 2 0 | 1 2 2 2 1  A,C,a,c
* * 4 * | 0 0 0 2 0 2 0 2 0 0 | 0 2 0 1 0 2 2 2 1 0 2 2 0 1 0 | 0 0 2 2 4 2 4 2 0 2 0 | 1 2 3 2 1  B,D,e,f
* * * 4 | 0 0 0 0 0 0 2 2 2 1 | 0 0 0 0 0 0 2 1 0 1 2 4 2 2 3 | 0 0 0 0 2 2 4 2 1 6 1 | 0 1 2 3 2  m,n,p,q
--------+---------------------+-------------------------------+-----------------------+----------
2 0 0 0 | 4 * * * * * * * * * | 2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 0 4 1 2 0 0 0 0 0 0 | 2 2 1 0 0  squares parallel
2 0 0 0 | * 2 * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 4 0 0 0 0 0 0 0 0 | 2 2 0 0 0  squares non-parallel (MQ, NP)
1 1 0 0 | * * 8 * * * * * * * | 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 | 0 1 2 1 1 2 1 0 0 0 0 | 1 2 1 1 0
1 0 1 0 | * * * 8 * * * * * * | 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 0 2 1 3 1 2 0 0 0 0 | 1 2 2 1 0
0 2 0 0 | * * * * 2 * * * * * | 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 | 0 1 0 0 0 4 0 0 1 0 0 | 0 2 0 2 0  Aa, Cc
0 1 1 0 | * * * * * 8 * * * * | 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 | 0 0 1 2 1 1 1 2 0 1 0 | 1 1 2 1 1
0 1 0 1 | * * * * * * 8 * * * | 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 | 0 0 0 0 1 2 1 1 1 2 0 | 0 1 1 2 1
0 0 1 1 | * * * * * * * 8 * * | 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 | 0 0 0 0 2 1 3 1 0 2 0 | 0 1 2 2 1
0 0 0 2 | * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 0 0 2 0 1 2 | 0 0 0 0 0 0 2 1 0 4 1 | 0 0 1 2 2  squares parallel
0 0 0 2 | * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 | 0 0 0 0 0 0 0 0 1 4 1 | 0 0 0 2 2  squares non-parallel (mq, np)
--------+---------------------+-------------------------------+-----------------------+----------
3 0 0 0 | 2 1 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 | 2 1 0 0 0
2 1 1 0 | 1 0 1 1 0 1 0 0 0 0 | * 8 * * * * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
2 1 0 0 | 0 1 2 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * | 0 1 2 0 0 0 0 0 0 0 0 | 1 2 0 0 0
2 0 1 0 | 1 0 2 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * | 0 0 2 0 2 0 0 0 0 0 0 | 1 2 1 0 0
1 2 0 0 | 0 0 2 0 1 0 0 0 0 0 | * * * * 4 * * * * * * * * * * | 0 1 0 0 0 2 0 0 0 0 0 | 0 2 0 1 0
1 1 1 0 | 0 0 1 1 0 1 0 0 0 0 | * * * * * 8 * * * * * * * * * | 0 0 1 1 0 1 1 0 0 0 0 | 1 1 1 1 0
1 1 1 1 | 0 0 1 1 0 0 1 1 0 0 | * * * * * * 8 * * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
1 0 2 1 | 0 0 0 2 0 0 0 2 0 0 | * * * * * * * 4 * * * * * * * | 0 0 0 0 2 0 2 0 0 0 0 | 0 1 2 1 0
0 2 2 0 | 0 0 0 0 0 4 0 0 0 0 | * * * * * * * * 2 * * * * * * | 0 0 0 2 0 0 0 2 0 0 0 | 1 0 2 0 1  ABCD, aecf
0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 | * * * * * * * * * 4 * * * * * | 0 0 0 0 0 2 0 0 1 0 0 | 0 1 0 2 0
0 1 1 1 | 0 0 0 0 0 1 1 1 0 0 | * * * * * * * * * * 8 * * * * | 0 0 0 0 1 1 0 1 0 1 0 | 0 1 1 1 1
0 1 1 2 | 0 0 0 0 0 1 1 1 1 0 | * * * * * * * * * * * 8 * * * | 0 0 0 0 0 0 1 1 0 1 0 | 0 0 1 1 1
0 1 0 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 0 1 2 0 | 0 0 0 2 1
0 0 1 2 | 0 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * * * * 4 * | 0 0 0 0 0 0 2 0 0 2 0 | 0 0 1 2 1
0 0 0 3 | 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2
--------+---------------------+-------------------------------+-----------------------+----------
4 0 0 0 | 4 2 0 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 2 0 0 0 0  tet MNPQ
2 2 0 0 | 0 1 4 0 1 0 0 0 0 0 | 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * | 0 2 0 0 0  tet
3 1 1 0 | 2 1 2 2 0 1 0 0 0 0 | 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 | * * 8 * * * * * * * * | 1 1 0 0 0  squippy
2 2 2 0 | 1 0 2 2 0 4 0 0 0 0 | 0 2 0 0 0 2 0 0 1 0 0 0 0 0 0 | * * * 4 * * * * * * * | 1 0 1 0 0  trip
2 1 2 1 | 1 0 1 3 0 1 1 2 0 0 | 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 | * * * * 8 * * * * * * | 0 1 1 0 0  trip
1 2 1 1 | 0 0 2 1 1 1 2 1 0 0 | 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 | * * * * * 8 * * * * * | 0 1 0 1 0  squippy
1 1 2 2 | 0 0 1 2 0 1 1 3 1 0 | 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 | * * * * * * 8 * * * * | 0 0 1 1 0  trip
0 2 2 2 | 0 0 0 0 0 4 2 2 1 0 | 0 0 0 0 0 0 0 0 1 0 2 2 0 0 0 | * * * * * * * 4 * * * | 0 0 1 0 1  trip
0 2 0 2 | 0 0 0 0 1 0 4 0 0 1 | 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 | * * * * * * * * 2 * * | 0 0 0 2 0  tet
0 1 1 3 | 0 0 0 0 0 1 2 2 2 1 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 | * * * * * * * * * 8 * | 0 0 0 1 1  squippy
0 0 0 4 | 0 0 0 0 0 0 0 0 4 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * 1 | 0 0 0 0 2  tet mnpq
--------+---------------------+-------------------------------+-----------------------+----------
4 2 2 0 | 4 2 4 4 0 4 0 0 0 0 | 4 4 2 2 0 4 0 0 1 0 0 0 0 0 0 | 1 0 4 2 0 0 0 0 0 0 0 | 2 * * * *  bidrap
3 2 2 1 | 2 1 4 4 1 2 2 2 0 0 | 1 2 2 2 2 2 2 1 0 1 2 0 0 0 0 | 0 1 2 0 2 2 0 0 0 0 0 | * 4 * * *  bidrap
2 2 3 2 | 1 0 2 4 0 4 2 4 1 0 | 0 2 0 1 0 2 2 2 1 0 2 2 0 1 0 | 0 0 0 1 2 0 2 1 0 0 0 | * * 4 * *  triddip
1 2 2 3 | 0 0 2 2 1 2 4 4 2 1 | 0 0 0 0 1 2 2 1 0 2 2 2 2 2 1 | 0 0 0 0 0 2 2 0 1 2 0 | * * * 4 *  bidrap
0 2 2 4 | 0 0 0 0 0 4 4 4 4 2 | 0 0 0 0 0 0 0 0 1 0 4 4 2 2 4 | 0 0 0 0 0 0 0 2 0 4 1 | * * * * 2  bidrap

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