Acronym dudeca
Name decachoron dual,
bi-apiculated pentachoron
Circumradius sqrt(2/3) = 0.816497
Inradius sqrt(5/24) = 0.456435
Dual deca

This polychoron can be obtained as the convex hull of the 2 pen compound (sted). Here all the edges of the former remain as long ones, while the short ones come in as interconnections of the 2 vertex set members. Each cell then joins a pair of adjacent vertices of one set to a pair of adjacent vertices of the other set, thus being a disphenoid.


Incidence matrix according to Dynkin symbol

o3m3m3o =
ao3oo3oo3oa&#zx   → height = 0, where a = sqrt(5/3) = 1.290994

o.3o.3o.3o.    | 5 *   4  4  0 | 12  6 | 12
.o3.o3.o3.o    | * 5   0  4  4 |  6 12 | 12
---------------+-----+----------+-------+---
a. .. .. ..    | 2 0 | 10  *  * |  3  0 |  3  a
oo3oo3oo3oo&#x | 1 1 |  * 20  * |  3  3 |  6  x
.. .. .. .a    | 0 2 |  *  * 10 |  0  3 |  3  a
---------------+-----+----------+-------+---
ao .. .. ..&#x | 2 1 |  1  2  0 | 30  * |  2
.. .. .. oa&#x | 1 2 |  0  2  1 |  * 30 |  2
---------------+-----+----------+-------+---
ao .. .. oa&#x | 2 2 |  1  4  1 |  2  2 | 30
or
o.3o.3o.3o.    & | 10   4  4 | 18 | 12
-----------------+----+-------+----+---
a. .. .. ..    & |  2 | 20  * |  3 |  3  a
oo3oo3oo3oo&#x   |  2 |  * 20 |  6 |  6  x
-----------------+----+-------+----+---
ao .. .. ..&#x & |  3 |  1  2 | 60 |  2
-----------------+----+-------+----+---
ao .. .. oa&#x   |  4 |  2  4 |  4 | 30

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