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xx xf&#x, xx ox&#f

Just as sadi was obtained from ex by an ico-symmetric diminishing, i.e. chopping off ikepy-caps, risadi is obtained from rox by an ico-symmetric diminishing, i.e. chopping off ikaid-caps. Accordingly the here occuring vertex figures too can be obtained as various diminishings by lacing edges from the vertex figure of rox, i.e. of pip.

Much more remarkable is that sadi allows for some of the same operations as regulars do: risadi is nothing but the rectification operation being applied to it. Moreover, it still is CRF.

Incidence matrix

rect( s3s4o3o )

mids(        . s4o .   ) | 144   * |   0   4   0   4 |  0   2  2   2  2   4  0 |  1  1  2  2  verf = xx xf&#x – at "head" of {5}
mids(  sefa( s3s . . ) ) |   * 288 |   2   2   2   0 |  1   2  0   4  0   1  1 |  2  0  1  2  verf = xx ox&#f – at "arms" & "legs" of {5}
-------------------------+---------+-----------------+-------------------------+------------
verf(        s3s . .   ) |   0   2 | 288   *   *   * |  1   0  0   2  0   0  0 |  2  0  0  1
verfA( sefa( s3s4o . ) ) |   1   1 |   * 576   *   * |  0   1  0   1  0   1  0 |  1  0  1  1
verfB( sefa( s3s4o . ) ) |   0   2 |   *   * 288   * |  0   1  0   1  0   0  1 |  1  0  1  1
verf(  sefa( . s4o3o ) ) |   2   0 |   *   *   * 288 |  0   0  1   0  1   1  0 |  0  1  1  1
-------------------------+---------+-----------------+-------------------------+------------
rect(        s3s . .   ) |   0   3 |   3   0   0   0 | 96   *  *   *  *   *  * |  2  0  0  0
rect(  sefa( s3s4o . ) ) |   1   2 |   0   2   1   0 |  * 288  *   *  *   *  * |  1  0  1  0
rect(  sefa( . s4o3o ) ) |   3   0 |   0   0   0   3 |  *   * 96   *  *   *  * |  0  1  1  0
verf(        s3s4o .   ) |   1   4 |   2   2   1   0 |  *   *  * 288  *   *  * |  1  0  0  1
verf(        . s4o3o   ) |   3   0 |   0   0   0   3 |  *   *  *   * 96   *  * |  0  1  0  1
verfA( sefa( s3s4o3o ) ) |   2   1 |   0   2   0   1 |  *   *  *   *  * 288  * |  0  0  1  1
verfB( sefa( s3s4o3o ) ) |   0   3 |   0   0   3   0 |  *   *  *   *  *   * 96 |  0  0  1  1
-------------------------+---------+-----------------+-------------------------+------------
rect(        s3s4o .   ) ♦   6  24 |  24  24  12   0 |  8  12  0  12  0   0  0 | 24  *  *  *
rect(        . s4o3o   ) ♦   6   0 |   0   0   0  12 |  0   0  4   0  4   0  0 |  * 24  *  *  (tet sym)
rect(  sefa( s3s4o3o ) ) ♦   3   3 |   0   6   3   3 |  0   3  1   0  0   3  1 |  *  * 96  *  (3-ap sym)
verf(        s3s4o3o   ) ♦   3   6 |   3   6   3   3 |  0   0  0   3  1   3  1 |  *  *  * 96