x3o3x      	-- co
      A          
                 
   x3x3o o3x3x   	-- tuta
   B             
                 
o3x3o x3o3x o3x3o	-- ico
C     D

     \     \     +-- srip
      \     +------- coatut
       +------------ oct

Just as nit can be considered the rectified hin, this metabidiminishing of the former can also be considered the rectification of the (meta-)bidhin.

Incidence matrix

co || pseudo tuta || ico   → both heights = 1/sqrt(2) = 0.707107

12  *  *  * |  4  4  0  0  0  0  0  0  0  0 | 2 2  4  2  4  2 0  0  0  0  0  0  0  0 0 0  0  0  0 0 | 1 2  4 2  4  1 0 0  0  0  0 0 0 0 0 0 | 2 2 2 0 0 0 A
 * 24  *  * |  0  2  1  2  2  1  2  0  0  0 | 0 0  2  2  1  2 1  3  1  2  2  2  1  2 0 0  0  0  0 0 | 0 2  1 1  3  2 1 1  3  2  1 1 0 0 0 0 | 1 1 3 1 1 0 B
 *  * 12  * |  0  0  0  0  0  2  0  4  4  0 | 0 0  0  0  0  0 0  0  1  4  4  0  0  0 2 2  2  2  4 0 | 0 2  0 0  0  0 0 2  2  4  2 0 1 2 2 1 | 1 0 2 1 2 1 C
 *  *  * 12 |  0  0  0  0  0  0  4  0  4  4 | 0 0  0  0  0  0 0  0  0  0  4  2  4  2 0 0  4  4  2 2 | 0 0  0 0  0  1 0 0  4  2  4 2 0 2 2 2 | 0 0 2 2 2 1 D
------------+-------------------------------+-------------------------------------------------------+---------------------------------------+------------
 2  0  0  0 | 24  *  *  *  *  *  *  *  *  * | 1 1  1  0  1  0 0  0  0  0  0  0  0  0 0 0  0  0  0 0 | 1 1  2 1  1  0 0 0  0  0  0 0 0 0 0 0 | 2 1 1 0 0 0
 1  1  0  0 |  * 48  *  *  *  *  *  *  *  * | 0 0  1  1  1  1 0  0  0  0  0  0  0  0 0 0  0  0  0 0 | 0 1  1 1  2  1 0 0  0  0  0 0 0 0 0 0 | 1 2 2 0 0 0
 0  2  0  0 |  *  * 12  *  *  *  *  *  *  * | 0 0  2  0  0  0 0  2  1  0  0  0  0  0 0 0  0  0  0 0 | 0 2  1 0  2  0 1 0  2  0  0 0 0 0 0 0 | 1 1 2 1 0 0 (6-6 ones of tut)
 0  2  0  0 |  *  *  * 24  *  *  *  *  *  * | 0 0  0  1  0  0 1  0  0  1  0  1  0  0 0 0  0  0  0 0 | 0 1  0 1  0  1 0 1  0  1  0 1 0 0 0 0 | 1 0 2 0 1 0 (3-6 ones of tut)
 0  2  0  0 |  *  *  *  * 24  *  *  *  *  * | 0 0  0  0  0  1 0  2  0  0  0  0  0  1 0 0  0  0  0 0 | 0 0  0 0  2  1 1 0  2  0  0 0 0 0 0 0 | 0 1 2 1 0 0 (inter tut ones)
 0  1  1  0 |  *  *  *  *  * 24  *  *  *  * | 0 0  0  0  0  0 0  0  1  2  2  0  0  0 0 0  0  0  0 0 | 0 2  0 0  0  0 0 1  2  2  1 0 0 0 0 0 | 1 0 2 1 1 0
 0  1  0  1 |  *  *  *  *  *  * 48  *  *  * | 0 0  0  0  0  0 0  0  0  0  1  1  1  1 0 0  0  0  0 0 | 0 0  0 0  0  1 0 0  2  1  1 1 0 0 0 0 | 0 0 2 1 1 0
 0  0  2  0 |  *  *  *  *  *  *  * 24  *  * | 0 0  0  0  0  0 0  0  0  1  0  0  0  0 1 1  0  0  1 0 | 0 1  0 0  0  0 0 1  0  1  0 0 1 1 1 0 | 1 0 1 0 1 1
 0  0  1  1 |  *  *  *  *  *  *  *  * 48  * | 0 0  0  0  0  0 0  0  0  0  1  0  0  0 0 0  1  1  1 0 | 0 0  0 0  0  0 0 0  1  1  1 0 0 1 1 1 | 0 0 1 1 1 1
 0  0  0  2 |  *  *  *  *  *  *  *  *  * 24 | 0 0  0  0  0  0 0  0  0  0  0  0  1  0 0 0  1  1  0 1 | 0 0  0 0  0  0 0 0  1  0  1 1 0 1 1 1 | 0 0 1 1 1 1
------------+-------------------------------+-------------------------------------------------------+---------------------------------------+------------
 3  0  0  0 |  3  0  0  0  0  0  0  0  0  0 | 8 *  *  *  *  * *  *  *  *  *  *  *  * * *  *  *  * * | 1 1  0 1  0  0 0 0  0  0  0 0 0 0 0 0 | 2 0 1 0 0 0
 4  0  0  0 |  4  0  0  0  0  0  0  0  0  0 | * 6  *  *  *  * *  *  *  *  *  *  *  * * *  *  *  * * | 1 0  2 0  0  0 0 0  0  0  0 0 0 0 0 0 | 2 1 0 0 0 0
 2  2  0  0 |  1  2  1  0  0  0  0  0  0  0 | * * 24  *  *  * *  *  *  *  *  *  *  * * *  *  *  * * | 0 1  1 0  1  0 0 0  0  0  0 0 0 0 0 0 | 1 1 1 0 0 0
 1  2  0  0 |  0  2  0  1  0  0  0  0  0  0 | * *  * 24  *  * *  *  *  *  *  *  *  * * *  *  *  * * | 0 1  0 1  0  1 0 0  0  0  0 0 0 0 0 0 | 1 0 2 0 0 0 (connect. med. nodes of lace city display)
 2  1  0  0 |  1  2  0  0  0  0  0  0  0  0 | * *  *  * 24  * *  *  *  *  *  *  *  * * *  *  *  * * | 0 0  1 1  1  0 0 0  0  0  0 0 0 0 0 0 | 1 1 1 0 0 0
 1  2  0  0 |  0  2  0  0  1  0  0  0  0  0 | * *  *  *  * 24 *  *  *  *  *  *  *  * * *  *  *  * * | 0 0  0 0  2  1 0 0  0  0  0 0 0 0 0 0 | 0 1 2 0 0 0 (using inter tut edge)
 0  3  0  0 |  0  0  0  3  0  0  0  0  0  0 | * *  *  *  *  * 8  *  *  *  *  *  *  * * *  *  *  * * | 0 0  0 1  0  0 0 1  0  0  0 1 0 0 0 0 | 1 0 1 0 1 0 (within tut)
 0  3  0  0 |  0  0  1  0  2  0  0  0  0  0 | * *  *  *  *  * * 24  *  *  *  *  *  * * *  *  *  * * | 0 0  0 0  1  0 1 0  1  0  0 0 0 0 0 0 | 0 1 1 1 0 0 (between tuts)
 0  2  1  0 |  0  0  1  0  0  2  0  0  0  0 | * *  *  *  *  * *  * 12  *  *  *  *  * * *  *  *  * * | 0 2  0 0  0  0 0 0  2  0  0 0 0 0 0 0 | 1 0 2 1 0 0
 0  2  2  0 |  0  0  0  1  0  2  0  1  0  0 | * *  *  *  *  * *  *  * 24  *  *  *  * * *  *  *  * * | 0 1  0 0  0  0 0 1  0  1  0 0 0 0 0 0 | 1 0 1 0 1 0
 0  1  1  1 |  0  0  0  0  0  1  1  0  1  0 | * *  *  *  *  * *  *  *  * 48  *  *  * * *  *  *  * * | 0 0  0 0  0  0 0 0  1  1  1 0 0 0 0 0 | 0 0 1 1 1 0
 0  2  0  1 |  0  0  0  1  0  0  2  0  0  0 | * *  *  *  *  * *  *  *  *  * 24  *  * * *  *  *  * * | 0 0  0 0  0  1 0 0  0  1  0 1 0 0 0 0 | 0 0 2 0 1 0 (connect. med. nodes of lace city display)
 0  1  0  2 |  0  0  0  0  0  0  2  0  0  1 | * *  *  *  *  * *  *  *  *  *  * 24  * * *  *  *  * * | 0 0  0 0  0  0 0 0  1  0  1 1 0 0 0 0 | 0 0 1 1 1 0
 0  2  0  1 |  0  0  0  0  1  0  2  0  0  0 | * *  *  *  *  * *  *  *  *  *  *  * 24 * *  *  *  * * | 0 0  0 0  0  1 0 0  2  0  0 0 0 0 0 0 | 0 0 2 1 0 0 (using inter tut edge)
 0  0  3  0 |  0  0  0  0  0  0  0  3  0  0 | * *  *  *  *  * *  *  *  *  *  *  *  * 8 *  *  *  * * | 0 1  0 0  0  0 0 0  0  0  0 0 1 1 0 0 | 1 0 1 0 0 1 (ABC-co inc.)
 0  0  3  0 |  0  0  0  0  0  0  0  3  0  0 | * *  *  *  *  * *  *  *  *  *  *  *  * * 8  *  *  * * | 0 0  0 0  0  0 0 1  0  0  0 0 1 0 1 0 | 1 0 0 0 1 1 (BC-trip inc)
 0  0  1  2 |  0  0  0  0  0  0  0  0  2  1 | * *  *  *  *  * *  *  *  *  *  *  *  * * * 24  *  * * | 0 0  0 0  0  0 0 0  1  0  0 0 0 1 0 1 | 0 0 1 1 0 1 (outer nodes of lace city display)
 0  0  1  2 |  0  0  0  0  0  0  0  0  2  1 | * *  *  *  *  * *  *  *  *  *  *  *  * * *  * 24  * * | 0 0  0 0  0  0 0 0  0  0  1 0 0 0 1 1 | 0 0 0 1 1 1 (inner nodes of lace city display)
 0  0  2  1 |  0  0  0  0  0  0  0  1  2  0 | * *  *  *  *  * *  *  *  *  *  *  *  * * *  *  * 24 * | 0 0  0 0  0  0 0 0  0  1  0 0 0 1 1 0 | 0 0 1 0 1 1
 0  0  0  3 |  0  0  0  0  0  0  0  0  0  3 | * *  *  *  *  * *  *  *  *  *  *  *  * * *  *  *  * 8 | 0 0  0 0  0  0 0 0  0  0  0 1 0 1 1 0 | 0 0 1 0 1 1
------------+-------------------------------+-------------------------------------------------------+---------------------------------------+------------
12  0  0  0 | 24  0  0  0  0  0  0  0  0  0 | 8 6  0  0  0  0 0  0  0  0  0  0  0  0 0 0  0  0  0 0 | 1 *  * *  *  * * *  *  *  * * * * * * | 2 0 0 0 0 0 co
 3  6  3  0 |  3  6  3  3  0  6  0  3  0  0 | 1 0  3  3  0  0 0  0  3  3  0  0  0  0 1 0  0  0  0 0 | * 8  * *  *  * * *  *  *  * * * * * * | 1 0 1 0 0 0 co
 4  2  0  0 |  4  4  1  0  0  0  0  0  0  0 | 0 1  2  0  2  0 0  0  0  0  0  0  0  0 0 0  0  0  0 0 | * * 12 *  *  * * *  *  *  * * * * * * | 1 1 0 0 0 0 trip
 3  3  0  0 |  3  6  0  3  0  0  0  0  0  0 | 1 0  0  3  3  0 1  0  0  0  0  0  0  0 0 0  0  0  0 0 | * *  * 8  *  * * *  *  *  * * * * * * | 1 0 1 0 0 0 oct
 2  3  0  0 |  1  4  1  0  2  0  0  0  0  0 | 0 0  1  0  1  2 0  1  0  0  0  0  0  0 0 0  0  0  0 0 | * *  * * 24  * * *  *  *  * * * * * * | 0 1 1 0 0 0 squippy
 1  4  0  1 |  0  4  0  2  2  0  4  0  0  0 | 0 0  0  2  0  2 0  0  0  0  0  2  0  2 0 0  0  0  0 0 | * *  * *  * 12 * *  *  *  * * * * * * | 0 0 2 0 0 0 oct
 0  4  0  0 |  0  0  2  0  4  0  0  0  0  0 | 0 0  0  0  0  0 0  4  0  0  0  0  0  0 0 0  0  0  0 0 | * *  * *  *  * 6 *  *  *  * * * * * * | 0 1 0 1 0 0 tet
 0  3  3  0 |  0  0  0  3  0  3  0  3  0  0 | 0 0  0  0  0  0 1  0  0  3  0  0  0  0 0 1  0  0  0 0 | * *  * *  *  * * 8  *  *  * * * * * * | 1 0 0 0 1 0 trip
 0  3  1  2 |  0  0  1  0  2  2  4  0  2  1 | 0 0  0  0  0  0 0  1  1  0  2  0  1  2 0 0  1  0  0 0 | * *  * *  *  * * * 24  *  * * * * * * | 0 0 1 1 0 0 oct
 0  2  2  1 |  0  0  0  1  0  2  2  1  2  0 | 0 0  0  0  0  0 0  0  0  1  2  1  0  0 0 0  0  0  1 0 | * *  * *  *  * * *  * 24  * * * * * * | 0 0 1 0 1 0 squippy
 0  1  1  2 |  0  0  0  0  0  1  2  0  2  1 | 0 0  0  0  0  0 0  0  0  0  2  0  1  0 0 0  0  1  0 0 | * *  * *  *  * * *  *  * 24 * * * * * | 0 0 0 1 1 0 tet
 0  3  0  3 |  0  0  0  3  0  0  6  0  0  3 | 0 0  0  0  0  0 1  0  0  0  0  3  3  0 0 0  0  0  0 1 | * *  * *  *  * * *  *  *  * 8 * * * * | 0 0 1 0 1 0 oct
 0  0  6  0 |  0  0  0  0  0  0  0 12  0  0 | 0 0  0  0  0  0 0  0  0  0  0  0  0  0 4 4  0  0  0 0 | * *  * *  *  * * *  *  *  * * 2 * * * | 1 0 0 0 0 1 oct
 0  0  3  3 |  0  0  0  0  0  0  0  3  6  3 | 0 0  0  0  0  0 0  0  0  0  0  0  0  0 1 0  3  0  3 1 | * *  * *  *  * * *  *  *  * * * 8 * * | 0 0 1 0 0 1 oct
 0  0  3  3 |  0  0  0  0  0  0  0  3  6  3 | 0 0  0  0  0  0 0  0  0  0  0  0  0  0 0 1  0  3  3 1 | * *  * *  *  * * *  *  *  * * * * 8 * | 0 0 0 0 1 1 oct
 0  0  2  4 |  0  0  0  0  0  0  0  0  8  4 | 0 0  0  0  0  0 0  0  0  0  0  0  0  0 0 0  4  4  0 0 | * *  * *  *  * * *  *  *  * * * * * 6 | 0 0 0 1 0 1 oct
------------+-------------------------------+-------------------------------------------------------+---------------------------------------+------------
12 12  6  0 | 24 24  6 12  0 12  0 12  0  0 | 8 6 12 12 12  0 4  0  6 12  0  0  0  0 4 4  0  0  0 0 | 1 4  6 4  0  0 0 4  0  0  0 0 1 0 0 0 | 2 * * * * * srip
 4  4  0  0 |  4  8  2  0  4  0  0  0  0  0 | 0 1  4  0  4  4 0  4  0  0  0  0  0  0 0 0  0  0  0 0 | 0 0  2 0  4  0 1 0  0  0  0 0 0 0 0 0 | * 6 * * * * bidrap
 3  9  3  3 |  3 12  3  6  6  6 12  3  6  3 | 1 0  3  6  3  6 1  3  3  3  6  6  3  6 1 0  3  0  3 1 | 0 1  0 1  3  3 0 0  3  3  0 1 0 1 0 0 | * * 8 * * * octaco
 0  4  2  4 |  0  0  2  0  4  4  8  0  8  4 | 0 0  0  0  0  0 0  4  2  0  8  0  4  4 0 0  4  4  0 0 | 0 0  0 0  0  0 1 0  4  0  4 0 0 0 0 1 | * * * 6 * * rap
 0  3  3  3 |  0  0  0  3  0  3  6  3  6  3 | 0 0  0  0  0  0 1  0  0  3  6  3  3  0 0 1  0  3  3 1 | 0 0  0 0  0  0 0 1  0  3  3 1 0 0 1 0 | * * * * 8 * traf
 0  0 12 12 |  0  0  0  0  0  0  0 24 48 24 | 0 0  0  0  0  0 0  0  0  0  0  0  0  0 8 8 24 24 24 8 | 0 0  0 0  0  0 0 0  0  0  0 0 2 8 8 6 | * * * * * 1 ico