Acronym	durat
Name	cubic-tegmatic tetracontateron, rectified-triacontiditeron dual, joined penteract
Dual	rat
Face vector	42, 240, 400, 240, 40
Confer	general polytopal classes: Catalan polytera
External links

This polyteron can be obtained as the tegum sum of a pent and a q-scaled tac. Here all the edges of the former remain as small ones, while the long ones come in as interconnections of the 2 vertex set members. In fact each facet itself is the tegum sum an edge of the latter with the fully orthogonal cube of the former, thus thereby becoming a taller variant of cute.

Incidence matrix according to Dynkin symbol

o3m3o3o4o =
qo3oo3oo3oo4ox&#zc   → height = 0, 
                       c = sqrt(5)/2 = 1.118034 (size of lacing edges)
                       y = sqrt(2) = 1.414214 (tip-to-tip diagonals)
(tegum sum of q-tac with pent)

o.3o.3o.3o.4o.     | 10  * ♦  16  0 |  32  0 |  24 |  8
.o3.o3.o3.o4.o     |  * 32 ♦   5  5 |  20 10 |  30 | 10
-------------------+-------+--------+--------+-----+---
oo3oo3oo3oo4oo&#c  |  1  1 | 160  * ♦   4  0 |   6 |  4
.. .. .. .. .x     |  0  2 |   * 80 ♦   4  4 |  12 |  6
-------------------+-------+--------+--------+-----+---
.. .. .. .. ox&#c  |  1  2 |   2  1 | 320  * |   3 |  3
.. .. .. .o4.x     |  0  4 |   0  4 |   * 80 |   3 |  3
-------------------+-------+--------+--------+-----+---
.. .. .. oo4ox&#c  |  1  4 |   4  4 |   4  1 | 240 |  2  variant of squippy
-------------------+-------+--------+--------+-----+---
qo .. oo3oo4ox&#zc |  2  8 |  16 12 |  24  6 |  12 | 40  variant of cute