Acronym	..., xFoFx3ooooo5xofox&#xt   (F=ff=x+f)
Name	bilunabirotundic rhombicosidodecahedron prism, castellated rhombicosidodecahedral prism
	© © ©
Coordinates	(τ3/2, 1/2, 1/2, τ/2)         & all permutations in all but last coordinate, all changes of sign (τ, τ2/2, τ/2, τ/2)             & even permutations in all but last coordinate, all changes of sign (τ2/2, 1+τ/2, 0, τ/2)        & even permutations in all but last coordinate, all changes of sign (these 3 describe the polar srids) (τ3/2, τ2/2, 0, 1/2)          & even permutations in all but last coordinate, all changes of sign (this describes the inscribed tropal τ2-ikes) (τ2/2, τ2/2, τ2/2, 0)         & all permutations in all but last coordinate, all changes of sign (τ3/2, 0, τ/2, 0)              & even permutations in all but last coordinate, all changes of sign (these 2 describe the inscribed equatorial τ-doe) where τ = (1+sqrt(5))/2
Face vector	164, 492, 424, 96
Confer	related CRFs: xoxFoFxox3oxoooooxo5ooxofoxoo&#xt
External links

It should by pointed out here, that in this figure the axial icosahedral symmetry cannot be replaced by e.g. an octahedral one, as it could for the ursachora. This is due to the existence of the equatorial type of vertices here. Those in fact are rigid, and so the attached bilbiroes have a fixed slope with respect to that partial complex of incident cells. But then, if trying to attach such a shard directly or parallely next to it, it obviously has to result in that here already used axial icosahedral symmetry.

It can also be obtained as a bistratic parabidiminishing of an expanded kaleido-faceting of ex, in fact of xoxFoFxox3oxoooooxo5ooxofoxoo&#xt.

Incidence matrix according to Dynkin symbol

xFoFx3ooooo5xofox&#xt   → height(1,2) = height(4,5) = (sqrt(5)-1)/4 = 0.309017
(F=ff=x+f)                height(2,3) = height(3,4) = 1/2
(srid || pseudo F-ike || pseudo f-doe || pseudo F-ike || srid)

o....3o....5o....     & | 120  *  * |   2   2   1   1  0 |  1  2  1   2   2  2 | 1  1  1  2
.o...3.o...5.o...     & |   * 24  * |   0   0   5   0  1 |  0  0  0   5   0  5 | 0  1  0  5
..o..3..o..5..o..       |   *  * 20 ♦   0   0   0   6  0 |  0  0  0   0   6  3 | 0  0  2  3
------------------------+-----------+--------------------+---------------------+-----------
x.... ..... .....     & |   2  0  0 | 120   *   *   *  * |  1  1  0   0   1  0 | 1  0  1  1
..... ..... x....     & |   2  0  0 |   * 120   *   *  * |  0  1  1   1   0  0 | 1  1  0  1
oo...3oo...5oo...&#x  & |   1  1  0 |   *   * 120   *  * |  0  0  0   2   0  1 | 0  1  0  2
o.o..3o.o..5o.o..&#x  & |   1  0  1 |   *   *   * 120  * |  0  0  0   0   2  1 | 0  0  1  2
.o.o.3.o.o.5.o.o.&#x    |   0  2  0 |   *   *   *   * 12 |  0  0  0   0   0  5 | 0  0  0  5
------------------------+-----------+--------------------+---------------------+-----------
x....3o.... .....     & |   3  0  0 |   3   0   0   0  0 | 40  *  *   *   *  * | 1  0  1  0
x.... ..... x....     & |   4  0  0 |   2   2   0   0  0 |  * 60  *   *   *  * | 1  0  0  1
..... o....5x....     & |   5  0  0 |   0   5   0   0  0 |  *  * 24   *   *  * | 1  1  0  0
..... ..... xo...&#x  & |   2  1  0 |   0   1   2   0  0 |  *  *  * 120   *  * | 0  1  0  1
x.o.. ..... .....&#x  & |   2  0  1 |   1   0   0   2  0 |  *  *  *   * 120  * | 0  0  1  1
ooooo3ooooo5ooooo&#xt   |   2  2  1 |   0   0   2   2  1 |  *  *  *   *   * 60 | 0  0  0  2
------------------------+-----------+--------------------+---------------------+-----------
x....3o....5x....     & ♦  60  0  0 |  60  60   0   0  0 | 20 30 12   0   0  0 | 2  *  *  *
..... oo...5xo...&#x  & ♦   5  1  0 |   0   5   5   0  0 |  0  0  1   5   0  0 | * 24  *  *
x.o..3o.o.. .....&#x  & ♦   3  0  1 |   3   0   0   3  0 |  1  0  0   0   3  0 | *  * 40  *
xFoFx ..... xofox&#xt   ♦   8  4  2 |   4   4   8   8  2 |  0  2  0   4   4  4 | *  *  * 30