Acronym ...
Name dodecateron dual
Circumradius sqrt(5/8) = 0.790569
Dual dot

This polyteron can be obtained as the convex hull of the 2 hix compound (stade). 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. And the 4-elements are the duals of triddip.


Incidence matrix according to Dynkin symbol

o3o3m3o3o =
ao3oo3oo3oo3oa&#zx   → height = 0, where a = sqrt(3/2) = 1.224745

o.3o.3o.3o.3o.     | 6 *   5  5  0 | 20 10 | 30 | 10
.o3.o3.o3.o3.o     | * 6   0  5  5 | 10 20 | 30 | 10
-------------------+-----+----------+-------+----+---
a. .. .. .. ..     | 2 0 | 15  *  *   4  0 |  6 |  4
oo3oo3oo3oo3oo&#x  | 1 1 |  * 30  *   4  4 | 12 |  6
.. .. .. .. .a     | 0 2 |  *  * 15   0  4 |  6 |  4
-------------------+-----+----------+-------+----+---
ao .. .. .. ..&#x  | 2 1 |  1  2  0 | 60  * |  3 |  3
.. .. .. .. oa&#x  | 1 2 |  0  2  1 |  * 60 |  3 |  3
-------------------+-----+----------+-------+----+---
ao .. .. .. oa&#x  | 2 2 |  1  4  1 |  2  2 | 90 |  2
-------------------+-----+----------+-------+----+---
ao3oo .. oo3oa&#zx  3 3 |  3  9  3 |  9  9 |  9 | 20
or
o.3o.3o.3o.3o.    & | 12   5  5 |  30 | 30 | 10
--------------------+----+-------+-----+----+---
a. .. .. .. ..    & |  2 | 30  *    4 |  6 |  4
oo3oo3oo3oo3oo&#x   |  2 |  * 30    8 | 12 |  6
--------------------+----+-------+-----+----+---
ao .. .. .. ..&#x & |  3 |  1  2 | 120 |  3 |  3
--------------------+----+-------+-----+----+---
ao .. .. .. oa&#x   |  4 |  2  4 |   4 | 90 |  2
--------------------+----+-------+-----+----+---
ao3oo .. oo3oa&#zx    6 |  6  9 |  18 |  9 | 20

oaoo3oooo3oooo3ooao&#xt   → outer heights = 2/sqrt(10) = 0.632456
                            inner height = 1/sqrt(10) = 0.316228
						    a = sqrt(3/2) = 1.224745
(pt || pseudo a-pen || dual pseudo a-pen || pt)

o...3o...3o...3o...        | 1 * * *  5 5  0  0 0  0 0 | 10 20  0  0  0  0 | 30  0  0 | 10  0
.o..3.o..3.o..3.o..        | * 5 * *  1 0  4  4 1  0 0 |  4  4 12  6  4  0 | 12 12  6 |  6  4
..o.3..o.3..o.3..o.        | * * 5 *  0 1  0  4 0  4 1 |  0  4  6 12  4  4 |  6 12 12 |  4  6
...o3...o3...o3...o        | * * * 1  0 0  0  0 5  0 5 |  0  0  0  0 20 10 |  0  0 30 |  0 10
---------------------------+---------+------------------+-------------------+----------+------
oo..3oo..3oo..3oo..&#x     | 1 1 0 0 | 5 *  *  * *  * *   4  4  0  0  0  0 | 12  0  0 |  6  0
o.o.3o.o.3o.o.3o.o.&#a     | 1 0 1 0 | * 5  *  * *  * *   0  4  0  0  0  0 |  6  0  0 |  4  0
.a.. .... .... ....        | 0 2 0 0 | * * 10  * *  * *   1  0  3  0  0  0 |  3  3  0 |  3  1
.oo.3.oo.3.oo.3.oo.&#x     | 0 1 1 0 | * *  * 20 *  * *   0  1  3  3  1  0 |  3  6  3 |  3  3
.o.o3.o.o3.o.o3.o.o&#a     | 0 1 0 1 | * *  *  * 5  * *   0  0  0  0  4  0 |  0  0  6 |  0  4
.... .... .... ..a.        | 0 0 2 0 | * *  *  * * 10 *   0  0  0  3  0  1 |  0  3  3 |  1  3
..oo3..oo3..oo3..oo&#x     | 0 0 1 1 | * *  *  * *  * 5   0  0  0  0  4  4 |  0  0 12 |  0  6
---------------------------+---------+------------------+-------------------+----------+------
oa.. .... .... ....&#x     | 1 2 0 0 | 2 0  1  0 0  0 0 | 10  *  *  *  *  * |  3  0  0 |  3  0
ooo.3ooo.3ooo.3ooo.&#(xxa) | 1 1 1 0 | 1 1  0  1 0  0 0 |  * 20  *  *  *  * |  3  0  0 |  3  0
.ao. .... .... ....&#x     | 0 2 1 0 | 0 0  1  2 0  0 0 |  *  * 30  *  *  * |  1  2  0 |  2  1
.... .... .... .oa.&#x     | 0 1 2 0 | 0 0  0  2 0  1 0 |  *  *  * 30  *  * |  0  2  1 |  1  2
.ooo3.ooo3.ooo3.ooo&#(xxa) | 0 1 1 1 | 0 0  0  1 1  0 1 |  *  *  *  * 20  * |  0  0  3 |  0  3
.... .... .... ..ao&#x     | 0 0 2 1 | 0 0  0  0 0  1 2 |  *  *  *  *  * 10 |  0  0  3 |  0  3
---------------------------+---------+------------------+-------------------+----------+------
oao. .... .... ....&#(ax)  | 1 2 1 0 | 2 1  1  2 0  0 0 |  1  2  1  0  0  0 | 30  *  * |  2  0
.ao. .... .... .oa.&#x     | 0 2 2 0 | 0 0  1  4 0  1 0 |  0  0  2  2  0  0 |  * 30  * |  1  1
.... .... .... .oao&#(ax)  | 0 1 2 1 | 0 0  0  2 1  1 2 |  0  0  0  1  2  1 |  *  * 30 |  0  2
---------------------------+---------+------------------+-------------------+----------+------
oao.3ooo. .... ooa.&#xt     1 3 2 0 | 3 2  3  6 0  1 0 |  3  6  6  3  0  0 |  6  3  0 | 10  *
.aoo .... .ooo3.oao&#xt     0 2 3 1 | 0 0  1  6 2  3 3 |  0  0  3  6  6  3 |  0  3  6 |  * 10

aooa oaoo3oooo3ooao&#xt   → outer heights = 1/4
                            inner height = 1/2
						    a = sqrt(3/2) = 1.224745

o... o...3o...3o...        & | 4 *  1  4  4 1  0  0 | 4  6 12  8  0 |  6 12 12 0 | 4  6
.o.. .o..3.o..3.o..        & | * 8  0  2  2 0  3  3 | 1  6 12  2  9 |  3 18  6 3 | 4  6
-----------------------------+-----+-----------------+---------------+------------+-----
a... .... .... ....        & | 2 0 | 2  *  * *  *  *  4  0  0  0  0 |  6  0  0 0 | 4  0
oo.. oo..3oo..3oo..&#x     & | 1 1 | * 16  * *  *  *  1  3  3  1  0 |  3  6  3 0 | 3  3
o.o. o.o.3o.o.3o.o.&#a     & | 1 1 | *  * 16 *  *  *  0  0  3  1  0 |  0  3  3 0 | 1  3
o..o o..o3o..o3o..o&#x       | 2 0 | *  *  * 2  *  *  0  0  0  8  0 |  0  0 12 0 | 0  6
.... .a.. .... ....        & | 0 2 | *  *  * * 12  *  0  2  0  0  2 |  1  4  0 1 | 2  2
.oo. .oo.3.oo.3.oo.&#x       | 0 2 | *  *  * *  * 12  0  0  4  0  4 |  0  8  2 2 | 2  4
-----------------------------+-----+-----------------+---------------+------------+-----
ao.. .... .... ....&#x     & | 2 1 | 1  2  0 0  0  0 | 8  *  *  *  * |  3  0  0 0 | 3  0
.... oa.. .... ....&#x     & | 1 2 | 0  2  0 0  1  0 | * 24  *  *  * |  1  2  0 0 | 2  1
ooo. ooo.3ooo.3ooo.&#(axx) & | 1 2 | 0  1  1 0  0  1 | *  * 48  *  * |  0  2  1 0 | 1  2
oo.o oo.o3oo.o3oo.o&#(axx) & | 2 1 | 0  1  1 1  0  0 | *  *  * 16  * |  0  0  3 0 | 0  3
.... .ao. .... ....&#x     & | 0 3 | 0  0  0 0  1  2 | *  *  *  * 24 |  0  2  0 1 | 1  2
-----------------------------+-----+-----------------+---------------+------------+-----
ao.. oa.. .... ....&#x     & | 2 2 | 1  4  0 0  1  0 | 2  2  0  0  0 | 12  *  * * | 2  0
.... oao. .... ....&#(ax)  & | 1 3 | 0  2  1 0  1  2 | 0  1  2  0  1 |  * 48  * * | 1  1
oooo oooo3oooo3oooo&#(ax)    | 2 2 | 0  2  2 1  0  1 | 0  0  2  2  0 |  *  * 24 * | 0  2
.... .ao. .... .oa.&#x       | 0 4 | 0  0  0 0  2  4 | 0  0  0  0  4 |  *  *  * 6 | 0  2
-----------------------------+-----+-----------------+---------------+------------+-----
aoo. oao.3ooo. ....&#xt    &  2 4 | 1  6  2 0  3  3 | 3  6  6  0  3 |  3  6  0 0 | 8  *
.... oaoo .... ooao&#(ax)     2 4 | 0  4  4 1  2  4 | 0  2  8  4  4 |  0  4  4 1 | * 12

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