Acronym ...
Name great-rhombated-pentachoron dual
Inradius 3/sqrt(85) = 0.325396
Dual grip

This polychoron can be obtained as the convex hull of 2 mutually dual pens and one rap of according ratios a, x and b respectively. Edges a and b become internal (pseudo). Only x and the 3 lacings remain. Each cell is a simplex with just a single mirror symmetry orthogonal to that edge x.


Incidence matrix according to Dynkin symbol

m3m3m3o =
aoo3obo3ooo3oox&#z(c,d,e)   → height = 0
                              a = 2/3 = 0.666667
                              b = 6/13 = 0.461538
                              c = lacing(1,2) = 2 sqrt(46)/39 = 0.347812
                              d = lacing(2,3) = sqrt(58)/13 = 0.585829
                              e = lacing(1,3) = 2/3 = 0.666667

o..3o..3o..3o..           | 5  * *   4  4  0  0 | 12  6  0 | 12
.o.3.o.3.o.3.o.           | * 10 *   2  0  3  0 |  6  0  3 |  6
..o3..o3..o3..o           | *  * 5   0  4  6  4 | 12 12 12 | 24
--------------------------+--------+-------------+----------+---
oo.3oo.3oo.3oo.&#c        | 1  1 0 | 20  *  *  * |  3  0  0 |  3
o.o3o.o3o.o3o.o&#e        | 1  0 1 |  * 20  *  * |  3  3  0 |  6
.oo3.oo3.oo3.oo&#d        | 0  1 1 |  *  * 30  * |  2  0  2 |  4
... ... ... ..x           | 0  0 2 |  *  *  * 10 |  0  3  3 |  6
--------------------------+--------+-------------+----------+---
ooo3ooo3ooo3ooo&#r(c,d,e) | 1  1 1 |  1  1  1  0 | 60  *  * |  2
... ... ... o.x&#e        | 1  0 2 |  0  2  0  1 |  * 30  * |  2
... ... ... .ox&#d        | 0  1 2 |  0  0  2  1 |  *  * 30 |  2
--------------------------+--------+-------------+----------+---
... ... ... oox&#(c,d,e)  | 1  1 2 |  1  2  2  1 |  2  1  1 | 60

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