©

    a                    g 
   b    c             h    
e    d               i    j
    f                      

Incidence matrix

pseudo tet || oct   → height = sqrt(5/8) = 0.790569

6 * |  4 1  2  2 0 | 2 2  4  4  4 1 1 0 | 1 4 2 2  a
* 4 |  0 0  3  3 3 | 0 0  3  3  3 3 3 3 | 0 3 3 3  g
----+--------------+--------------------+--------
2 0 | 12 *  *  * * | 1 1  1  1  0 0 0 0 | 1 1 1 1  ab x
2 0 |  * 3  *  * * | 0 0  0  0  4 0 0 0 | 0 4 0 0  af q
1 1 |  * * 12  * * | 0 0  2  0  1 1 0 0 | 0 2 0 2  ag x
1 1 |  * *  * 12 * | 0 0  0  2  1 0 1 0 | 0 2 2 0  ai q
0 2 |  * *  *  * 6 | 0 0  0  0  0 1 1 2 | 0 0 2 2  gh x
----+--------------+--------------------+--------
3 0 |  3 0  0  0 0 | 4 *  *  *  * * * * | 1 0 1 0  abc xxx = verf(tet)
3 0 |  3 0  0  0 0 | * 4  *  *  * * * * | 1 0 0 1  abe xxx = verf(tet)
2 1 |  1 0  2  0 0 | * * 12  *  * * * * | 0 1 0 1  abg xxx = verf(tet)
2 1 |  1 0  0  2 0 | * *  * 12  * * * * | 0 1 1 0  abj xqq = verf(trip)
2 1 |  0 1  1  1 0 | * *  *  * 12 * * * | 0 2 0 0  afg xqq = verf(trip)
1 2 |  0 0  2  0 1 | * *  *  *  * 6 * * | 0 0 0 2  agh xxx = verf(tet)
1 2 |  0 0  0  2 1 | * *  *  *  * * 6 * | 0 0 2 0  aij xqq = verf(trip)
0 3 |  0 0  0  0 3 | * *  *  *  * * * 4 | 0 0 1 1  ghi xxx = verf(tet)
----+--------------+--------------------+--------
6 0 | 12 0  0  0 0 | 4 4  0  0  0 0 0 0 | 1 * * *  abcdef oct = verf(hex)
4 2 |  2 2  4  4 0 | 0 0  2  2  4 0 0 0 | * 6 * *  abdfgj verf(firp)
3 3 |  3 0  0  6 3 | 1 0  0  3  0 0 3 1 | * * 4 *  abchij verf(firp)
3 3 |  3 0  6  0 3 | 0 1  3  0  0 3 0 1 | * * * 4  abeghi oct = verf(hex)

or
10 |  6  3 |  3  6  9 | 3  6
---+-------+----------+-----
 2 | 30  * |  1  2  1 | 2  2  x
 2 |  * 15 |  0  0  4 | 0  4  q
---+-------+----------+-----
 3 |  3  0 | 10  *  * | 2  0  xxx = verf(tet)
 3 |  3  0 |  * 20  * | 1  1  xxx = verf(tet)
 3 |  1  2 |  *  * 30 | 0  2  xqq = verf(trip)
---+-------+----------+-----
 6 | 12  0 |  4  4  0 | 5  *  oct = verf(hex)
 6 |  6  6 |  0  2  6 | * 10  verf(firp)