Acronym	tibbid (alt.: durap)
Name	triangular-bipyramidal decachoron, rectified-pentachoron dual, surtegmated pentachoron, joined pentachoron
	©   ©
Inradius	1/sqrt(15) = 0.258199
Dual	rap
Face vector	10, 30, 30, 10
Confer	general polytopal classes: Catalan polychora
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This polychoron can be obtained from the compound of a unit pen and a scaled dual pen, when choosing the edge center radius of the first pen and the triangle center radius of second pen to be equal. Then the convex hull therefrom results in this polychoron, and the edges of the former resp. the orthogonal triangles of the latter will serve as diametrals of the cells of this hull polychoron.

All c edges, provided in the below description, only qualify as pseudo edges wrt. the full polychoron. In fact those are the tip-to-tip diametrals of the cells, which all are identical bipyramids, which here happen to be m m3o (the dual of trip). As can be read from the incidence matrix, the polar tips of these bipyramids join by 4 in a tetrahedral vertex figure, while the equatorial vertices of those bipyramids join by 6 in a cubical vertex figure.

Because o3m3o3o is derived by some secondary process only (rectification followed by dualisation), instead of a primary Wythoff construction, it is much more remarkable that it still allows for rectification (oq3oo3qo3oc&zx). This is because the truncational depth of the second vertex type (in the below incidence matrix) for a rectification scenario is easily settled at the second edge type (providing the mid points at those x-edges). But then the same truncational hyperplanes would define corresponding intersection points on the y-edges as well. And those points then could be matched in a rectificational sense by truncation hyperplanes of according depth wrt. the first vertex set.

The pictures above display a projection, a single cell, an unfolded net, and a section movie running along its diagonal from a cubical vertex to its opposite tetrahedral vertex.

Incidence matrix according to Dynkin symbol

o3m3o3o =
co3oo3oo3ox&#zy   → height = 0
                    c = 2/3 (tip-to-tip diametrals)
                    y = 2/3 (lacing edges)

o.3o.3o.3o.     | 5 * ♦  4  0 |  6 |  4
.o3.o3.o3.o     | * 5 ♦  4  4 | 12 |  6
----------------+-----+-------+----+---
oo3oo3oo3oo&#y  | 1 1 | 20  * |  3 |  3
.. .. .. .x     | 0 2 |  * 10 |  3 |  3
----------------+-----+-------+----+---
.. .. .. ox&#y  | 1 2 |  2  1 | 30 |  2
----------------+-----+-------+----+---
co .. oo3ox&#zy ♦ 2 3 |  6  3 |  6 | 10