Acronym	sadi   (alt.: idex)
Name	snub icositetrachoron, snub disicositetrachoron, semistruncated icositetrachoron, icositetradiminished hexacosachoron
Cross sections	©
Circumradius	(1+sqrt(5))/2 = 1.618034
Coordinates	(τ2/2, τ/2, 1/2, 0)    & even permutations, all changes of sign where τ = (1+sqrt(5))/2
Vertex figure	©
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: ike tet sadi 24 120 )
Confer	related CRFs: idsrix   idprix   idsid pixhi   bidex   segmentochora: ikepy
External links

Sadi is a special diminishing of the hexacosachoron (ex). In fact, into ex an f-ico can be vertex inscribed. If those 24 vertices of ex would be chopped off, resulting in an icosahedral section each, the outcome is nothing but sadi.

Incidence matrix according to Dynkin symbol

s3s4o3o

demi( . . . . ) | 96 ♦   3   6 |  3   9  3 |  3  1  4
----------------+----+---------+-----------+---------
      . s4o .   |  2 | 144   * |  0   2  2 |  1  1  2
sefa( s3s . . ) |  2 |   * 288 |  1   2  0 |  2  0  1
----------------+----+---------+-----------+---------
      s3s . .   ♦  3 |   0   3 | 96   *  * |  2  0  0
sefa( s3s4o . ) |  3 |   1   2 |  * 288  * |  1  0  1
sefa( . s4o3o ) |  3 |   3   0 |  *   * 96 |  0  1  1
----------------+----+---------+-----------+---------
      s3s4o .   ♦ 12 |   6  24 |  8  12  0 | 24  *  *
      . s4o3o   ♦  4 |   6   0 |  0   0  4 |  * 24  *
sefa( s3s4o3o ) ♦  4 |   3   3 |  0   3  1 |  *  * 96

s3s3s4o

demi( . . . . ) | 96 ♦  2  1  2   4 |  1  2   6  3  3 |  2  1 1  4
----------------+----+--------------+-----------------+-----------
      s 2 s .   |  2 | 96  *  *   * |  0  0   2  2  0 |  1  1 0  2
      . . s4o   |  2 |  * 48  *   * |  0  0   0  2  2 |  0  1 1  2
sefa( s3s . . ) |  2 |  *  * 96   * |  1  0   2  0  0 |  2  0 0  1
sefa( . s3s . ) |  2 |  *  *  * 192 |  0  1   1  0  1 |  1  0 1  1
----------------+----+--------------+-----------------+-----------
      s3s . .   ♦  3 |  0  0  3   0 | 32  *   *  *  * |  2  0 0  0
      . s3s .   ♦  3 |  0  0  0   3 |  * 64   *  *  * |  1  0 1  0
sefa( s3s3s . ) |  3 |  1  0  1   1 |  *  * 192  *  * |  1  0 0  1
sefa( s 2 s4o ) |  3 |  2  1  0   0 |  *  *   * 96  * |  0  1 0  1
sefa( . s3s4o ) |  3 |  0  1  0   2 |  *  *   *  * 96 |  0  0 1  1
----------------+----+--------------+-----------------+-----------
      s3s3s .   ♦ 12 |  6  0 12  12 |  4  4  12  0  0 | 16  * *  *
      s 2 s4o   ♦  4 |  4  2  0   0 |  0  0   0  4  0 |  * 24 *  *
      . s3s4o   ♦ 12 |  0  6  0  24 |  0  8   0  0 12 |  *  * 8  *
sefa( s3s3s4o ) ♦  4 |  2  1  1   2 |  0  0   2  1  1 |  *  * * 96

s3s3s *b3s

demi( . . .    . ) | 96 ♦  1  1  1  2  2  2 |  1  1  1  3  3  3  3 | 1 1  1 1  4
-------------------+----+-------------------+----------------------+------------
      s 2 s    .   |  2 | 48  *  *  *  *  * |  0  0  0  2  0  2  0 | 1 0  1 0  2
      s 2 .    s   |  2 |  * 48  *  *  *  * |  0  0  0  0  2  2  0 | 0 1  1 0  2
      . 2 s    s   |  2 |  *  * 48  *  *  * |  0  0  0  0  0  2  2 | 0 0  1 1  2
sefa( s3s .    . ) |  2 |  *  *  * 96  *  * |  1  0  0  1  1  0  0 | 1 1  0 0  1
sefa( . s3s    . ) |  2 |  *  *  *  * 96  * |  0  1  0  1  0  0  1 | 1 0  0 1  1
sefa( . s . *b3s ) |  2 |  *  *  *  *  * 96 |  0  0  1  0  1  0  1 | 0 1  0 1  1
-------------------+----+-------------------+----------------------+------------
      s3s .    .   ♦  3 |  0  0  0  3  0  0 | 32  *  *  *  *  *  * | 1 1  0 0  0
      . s3s    .   ♦  3 |  0  0  0  0  3  0 |  * 32  *  *  *  *  * | 1 0  0 1  0
      . s . *b3s   ♦  3 |  0  0  0  0  0  3 |  *  * 32  *  *  *  * | 0 1  0 1  0
sefa( s3s3s    . ) |  3 |  1  0  0  1  1  0 |  *  *  * 96  *  *  * | 1 0  0 0  1
sefa( s3s . *b3s ) |  3 |  0  1  0  1  0  1 |  *  *  *  * 96  *  * | 0 1  0 0  1
sefa( s 2 s  2 s ) |  3 |  1  1  1  0  0  0 |  *  *  *  *  * 96  * | 0 0  1 0  1
sefa( . s3s *b3s ) |  3 |  0  0  1  0  1  1 |  *  *  *  *  *  * 96 | 0 0  0 1  1
-------------------+----+-------------------+----------------------+------------
      s3s3s    .   ♦ 12 |  6  0  0 12 12  0 |  4  4  0 12  0  0  0 | 8 *  * *  *
      s3s . *b3s   ♦ 12 |  0  6  0 12  0 12 |  4  0  4  0 12  0  0 | * 8  * *  *
      s 2 s  2 s   ♦  4 |  2  2  2  0  0  0 |  0  0  0  0  0  4  0 | * * 24 *  *
      . s3s *b3s   ♦ 12 |  0  0  6  0 12 12 |  0  4  4  0  0  0 12 | * *  * 8  *
sefa( s3s3s *b3s ) ♦  4 |  1  1  1  1  1  1 |  0  0  0  1  1  1  1 | * *  * * 96