Acronym	dutip
Name	truncated-pentachoron dual, apiculated pentachoron, tetrakis pentachoron
	©
Inradius	3/sqrt(160) = 0.237171
Dual	tip
Face vector	10, 30, 40, 20
Confer	general polytopal classes: Catalan polychora
External links

This polychoron can be obtained as the convex hull of 2 mutually dual pens of according ratio c:x = 3/7. For this polychoron all the edges of the larger pen, x, remain as long ones, while its short ones, y, come in as lacings between the 2 vertex set members. Each cell then adjoins one vertex of that smaller pen to one of the nearby triangles of the larger one.

Incidence matrix according to Dynkin symbol

m3m3o3o =
co3oo3oo3ox&#zy   → height = 0
                    c = 3/7 = 0.428571
                    y = sqrt(19)/7 = 0.622700

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