Acronym idimex Name spid-diminished ex,icosidiminished ex Circumradius (1+sqrt(5))/2 = 1.618034 Vertex figure teddi, mibdi Dihedral angles at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512° at {3} between ike and tet:   arccos[-sqrt(5/8)] = 142.238756° Confer uniform relative: ex   compounds: dopix   related CRFs: oFxx3xxof3foxo3oofx&#zx   ridimex   tidimex   idimsrix   idim sidpixhi   idimsrahi   segmentochora: ikepy   general polytopal classes: subsymmetrical diminishings   Blind polytopes

This orbiform polychoron is a special diminishing of the hexacosachoron (ex). In fact, into ex an f-spid can be vertex inscribed. If those 20 vertices of ex would be chopped off, resulting in an icosahedral section each, the outcome is just that.

In fact, within pentic subsymmetry ex can be given as xffoo3oxoof3fooxo3ooffx&#zx. The 3rd level here just describes that vertex inscribed f-spid. Therefore the remaining 4 levels xf.oo3ox.of3fo.xo3oo.fx&#zx would describe this polychoron.

Because idimex is derived by some secondary process only (diminishing), instead of a primary Wythoff construction and moreover itself not even is a uniform figure, it is much more remarkable that it still allows for truncation (tisadi) and rectification (risadi). And even more interesting, both these polychora then happen to come out to be CRF polytopes as well!

That ex inscribed f-spid btw. is nothing but a single out of 60 such components of the uniform compound dopix.

Incidence matrix according to Dynkin symbol

```xfoo3oxof3foxo3oofx&#zx   → all heights = 0 – except those of the not existing lacing(2,3)

o...3o...3o...3o...     & | 60  * ♦  2   2   2   4  0 |  1  1   4   6   8  0 |  2  2  2   6  0
.o..3.o..3.o..3.o..     & |  * 40 ♦  0   3   3   0  3 |  0  3   3   0   6  3 |  1  0  3   3  1
--------------------------+-------+-------------------+----------------------+----------------
x... .... .... ....     & |  2  0 | 60   *   *   *  * |  1  0   2   2   0  0 |  2  1  0   2  0
oo..3oo..3oo..3oo..&#x  & |  1  1 |  * 120   *   *  * |  0  1   0   0   2  0 |  0  0  2   1  0
o.o.3o.o.3o.o.3o.o.&#x  & |  1  1 |  *   * 120   *  * |  0  0   2   0   2  0 |  1  0  1   2  0
o..o3o..o3o..o3o..o&#x    |  2  0 |  *   *   * 120  * |  0  0   0   2   2  0 |  0  1  1   2  0
.... .x.. .... ....     & |  0  2 |  *   *   *   * 60 |  0  1   0   0   0  2 |  0  0  2   0  1
--------------------------+-------+-------------------+----------------------+----------------
x...3o... .... ....     & |  3  0 |  3   0   0   0  0 | 20  *   *   *   *  * |  2  0  0   0  0
.... ox.. .... ....&#x  & |  1  2 |  0   2   0   0  1 |  * 60   *   *   *  * |  0  0  2   0  0
x.o. .... .... ....&#x  & |  2  1 |  1   0   2   0  0 |  *  * 120   *   *  * |  1  0  0   1  0
x..o .... .... ....&#x  & |  3  0 |  1   0   0   2  0 |  *  *   * 120   *  * |  0  1  0   1  0
oo.o3oo.o3oo.o3oo.o&#x  & |  2  1 |  0   1   1   1  0 |  *  *   *   * 240  * |  0  0  1   1  0
.... .x..3.o.. ....     & |  0  3 |  0   0   0   0  3 |  *  *   *   *   * 40 |  0  0  1   0  1
--------------------------+-------+-------------------+----------------------+----------------
x.o.3o.o. .... ....&#x  & ♦  3  1 |  3   0   3   0  0 |  1  0   3   0   0  0 | 40  *  *   *  *
x..o .... .... o..x&#x    ♦  4  0 |  2   0   0   4  0 |  0  0   0   4   0  0 |  * 30  *   *  *
.... oxof3foxo ....&#xt   ♦  6  6 |  0  12   6   6  6 |  0  6   0   0  12  2 |  *  * 20   *  *  tower b-a-d-c
.... .... .... oo.x&#x  & ♦  3  1 |  1   1   2   2  0 |  0  0   1   1   2  0 |  *  *  * 120  *
.... .x..3.o..3.o..     & ♦  0  4 |  0   0   0   0  6 |  0  0   0   0   0  4 |  *  *  *   * 10
```