Acronym ...
Name triangle duotegum,
dual of triangle duoprism
Circumradius 3/sqrt(8) = 1.060660
Dual triddip
External
links
hedrondude  

This polychoron can be obtained as the convex hull of the 2 fully orthogonal a-triangles.


Incidence matrix according to Dynkin symbol

m3o2m3o =
ao3oo oa3oo&#zx   → height = 0, where a = sqrt(3/2) = 1.224745

o.3o. o.3o.     | 3 *  2 3 0 | 6 3 | 6
.o3.o .o3.o     | * 3  0 3 2 | 3 6 | 6
----------------+-----+-------+-----+--
a. .. .. ..     | 2 0 | 3 * * | 3 0 | 3
oo3oo oo3oo&#x  | 1 1 | * 9 * | 2 2 | 4
.. .. .a ..     | 0 2 | * * 3 | 0 3 | 3
----------------+-----+-------+-----+--
ao .. .. ..&#x  | 2 1 | 1 2 0 | 9 * | 2
.. .. oa ..&#x  | 1 2 | 0 2 1 | * 9 | 2
----------------+-----+-------+-----+--
ao .. oa ..&#x  | 2 2 | 1 4 1 | 2 2 | 9
or
o.3o. o.3o.     & | 6  2 3 |  9 | 6
------------------+---+-----+----+--
a. .. .. ..     & | 2 | 6 * |  3 | 3
oo3oo oo3oo&#x    | 2 | * 9 |  4 | 4
------------------+---+-----+----+--
ao .. .. ..&#x  & | 3 | 1 2 | 18 | 2
------------------+---+-----+----+--
ao .. oa ..&#x    | 4 | 2 4 |  4 | 9

ooa oao3ooo&#xt   → height(1,2) = 1/sqrt(3) = 0.577350,
                    height(2,3) = 1/sqrt(12) = 0.288675,
                    a = sqrt(3/2) = 1.224745
(pt || pseudo a-{3} || perp a-line)

o.. o..3o..        | 1 * *  3 2 0 0 0 | 3 6 0 0 | 6 0
.o. .o.3.o.        | * 3 *  1 0 2 2 0 | 2 2 1 4 | 4 2
..o ..o3..o        | * * 2  0 1 0 3 1 | 0 3 3 3 | 3 3
-------------------+-------+-----------+---------+----
oo. oo.3oo.&#x     | 1 1 0 | 3 * * * * | 2 2 0 0 | 4 0
o.o o.o3o.o&#a     | 1 0 1 | * 2 * * * | 0 3 0 0 | 3 0
... .a. ...        | 0 2 0 | * * 3 * * | 1 0 0 2 | 2 1
.oo .oo3.oo&#x     | 0 1 1 | * * * 6 * | 0 1 1 2 | 2 2
..a ... ...        | 0 0 2 | * * * * 1 | 0 0 3 0 | 0 3
-------------------+-------+-----------+---------+----
... oa. ...&#x     | 1 2 0 | 2 0 1 0 0 | 3 * * * | 2 0
ooo ooo3ooo&#(axx) | 1 1 1 | 1 1 0 1 0 | * 6 * * | 2 0
.oa ... ...&#x     | 0 1 2 | 0 0 0 2 1 | * * 3 * | 0 2
... .ao ...&#x     | 0 2 1 | 0 0 1 2 0 | * * * 6 | 1 1
-------------------+-------+-----------+---------+----
... oao ...&#(ax)  | 1 2 1 | 2 1 1 2 0 | 1 2 0 1 | 6 *
.oa .ao ...&#x     | 0 2 2 | 0 0 1 4 1 | 0 0 2 2 | * 3

oaoo ooao&#(ax)   → height(1,2) = height(3,4) = sqrt(5/8) = 0.790569, laced x
                    height(1,3) = height(2,4) = 3/sqrt(8) = 1.060660, laced a
                    height(2,3) = 1/2, laced x
                    height(1,4) = 1
                    a = sqrt(3/2) = 1.224745

o... o...        | 1 * * *  2 2 1 0 0 0 0 0 | 1 4 2 2 0 0 0 0 | 2 4 0 0
.o.. .o..        | * 2 * *  1 0 0 1 2 1 0 0 | 1 2 1 0 2 1 2 0 | 2 2 1 1
..o. ..o.        | * * 2 *  0 1 0 0 2 0 1 1 | 0 2 0 1 1 2 2 1 | 1 2 1 2
...o ...o        | * * * 1  0 0 1 0 0 2 0 2 | 0 0 2 2 0 0 4 1 | 0 4 0 2
-----------------+---------+-----------------+-----------------+--------
oo.. oo..&#x     | 1 1 0 0 | 2 * * * * * * * | 1 2 1 0 0 0 0 0 | 2 2 0 0
o.o. o.o.&#a     | 1 0 1 0 | * 2 * * * * * * | 0 2 0 1 0 0 0 0 | 1 2 0 0
o..o o..o&#x     | 1 0 0 1 | * * 1 * * * * * | 0 0 2 2 0 0 0 0 | 0 4 0 0
.a.. ....        | 0 2 0 0 | * * * 1 * * * * | 1 0 0 0 2 0 0 0 | 2 0 1 0
.oo. .oo.&#x     | 0 1 1 0 | * * * * 4 * * * | 0 1 0 0 1 1 1 0 | 1 1 1 1
.o.o .o.o&#a     | 0 1 0 1 | * * * * * 2 * * | 0 0 1 0 0 0 2 0 | 0 2 0 1
.... ..a.        | 0 0 2 0 | * * * * * * 1 * | 0 0 0 0 0 2 0 1 | 0 0 1 2
..oo ..oo&#x     | 0 0 1 1 | * * * * * * * 2 | 0 0 0 1 0 0 2 1 | 0 2 0 2
-----------------+---------+-----------------+-----------------+--------
oa.. ....&#x     | 1 2 0 0 | 2 0 0 1 0 0 0 0 | 1 * * * * * * * | 2 0 0 0
ooo. ooo.&#(axx) | 1 1 1 0 | 1 1 0 0 1 0 0 0 | * 4 * * * * * * | 1 1 0 0
oo.o oo.o&#(axx) | 1 1 0 1 | 1 0 1 0 0 1 0 0 | * * 2 * * * * * | 0 2 0 0
o.oo o.oo&#(axx) | 1 0 1 1 | 0 1 1 0 0 0 0 1 | * * * 2 * * * * | 0 2 0 0
.ao. ....&#(axx) | 0 2 1 0 | 0 0 0 1 2 0 0 0 | * * * * 2 * * * | 1 0 1 0
.... .oa.&#(axx) | 0 1 2 0 | 0 0 0 0 2 0 1 0 | * * * * * 2 * * | 0 0 1 1
.ooo .ooo&#(axx) | 0 1 1 1 | 0 0 0 0 1 1 0 1 | * * * * * * 4 * | 0 1 0 1
.... ..ao&#x     | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * 1 | 0 0 0 2
-----------------+---------+-----------------+-----------------+--------
oao. ....&#(ax)  | 1 2 1 0 | 2 1 0 1 2 0 0 0 | 1 2 0 0 1 0 0 0 | 2 * * *
oooo oooo&#(ax)  | 1 1 1 1 | 1 1 1 0 1 1 0 1 | 0 1 1 1 0 0 1 0 | * 4 * *
.ao. .oa.&#x     | 0 2 2 0 | 0 0 0 1 4 0 1 0 | 0 0 0 0 2 2 0 0 | * * 1 *
.... .oao&#(ax)  | 0 1 2 1 | 0 0 0 0 2 1 1 2 | 0 0 0 0 0 1 2 1 | * * * 2

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