Acronym ...
Name triangular duoexpandoprism
Circumradius sqrt[(a2+3b2)/3]
Lace city
in approx. ASCII-art 
   a3o     a3o   
       b3b       
                 
a3o           a3o
   b3b     b3b   
                 
   a3o     a3o
Face vector 36, 108, 120, 48
External
links 		polytopewiki  

Incidence matrix according to Dynkin symbol

ab3ob ba3bo&#zc   → height = 0
                    2a < 3b (else a3o - b3b - a3o becomes collinear)
                    3c2 = 2a2-6ab+6b2
(c-laced tegum sum of 2 (a,b)-thiddips)

o.3o. o.3o.    | 18  * |  2 1 1  2 0 0  0 | 1 2 2  2  1  2  2 0 0 0 | 1 1 2 2 1 1 0 0
.o3.o .o3.o    |  * 18 |  0 0 0  2 1 1  2 | 0 0 0  2  2  2  1 2 2 1 | 0 0 2 1 2 1 1 1
---------------+-------+------------------+-------------------------+----------------
a. .. .. ..    |  2  0 | 18 * *  * * *  * | 1 1 1  1  0  0  0 0 0 0 | 1 1 1 1 0 0 0 0  a
.. .. b. ..    |  2  0 |  * 9 *  * * *  * | 0 2 0  0  0  0  2 0 0 0 | 1 0 2 0 1 0 0 0  b
.. .. .. b.    |  2  0 |  * * 9  * * *  * | 0 0 2  0  0  2  0 0 0 0 | 0 1 0 2 0 1 0 0  b
oo3oo oo3oo&#c |  1  1 |  * * * 36 * *  * | 0 0 0  1  1  1  1 0 0 0 | 0 0 1 1 1 1 0 0  c
.b .. .. ..    |  0  2 |  * * *  * 9 *  * | 0 0 0  2  0  0  0 2 0 0 | 0 0 2 1 0 0 1 0  b
.. .b .. ..    |  0  2 |  * * *  * * 9  * | 0 0 0  0  2  0  0 0 2 0 | 0 0 0 0 2 1 0 1  b
.. .. .a ..    |  0  2 |  * * *  * * * 18 | 0 0 0  0  0  1  0 1 1 1 | 0 0 1 0 1 0 1 1  a
---------------+-------+------------------+-------------------------+----------------
a.3o. .. ..    |  3  0 |  3 0 0  0 0 0  0 | 6 * *  *  *  *  * * * * | 1 1 0 0 0 0 0 0  aaa
a. .. b. ..    |  4  0 |  2 2 0  0 0 0  0 | * 9 *  *  *  *  * * * * | 1 0 1 0 0 0 0 0  abab
a. .. .. b.    |  4  0 |  2 0 2  0 0 0  0 | * * 9  *  *  *  * * * * | 0 1 0 1 0 0 0 0  abab
ab .. .. ..&#c |  2  2 |  1 0 0  2 1 0  0 | * * * 18  *  *  * * * * | 0 0 1 1 0 0 0 0  acbc
.. ob .. ..&#c |  1  2 |  0 0 0  2 0 1  0 | * * *  * 18  *  * * * * | 0 0 0 0 1 1 0 0  bbc
.. .. ba ..&#c |  2  2 |  0 0 1  2 0 0  1 | * * *  *  * 18  * * * * | 0 0 1 0 1 0 0 0  acbc
.. .. .. bo&#c |  2  1 |  0 1 0  2 0 0  0 | * * *  *  *  * 18 * * * | 0 0 0 1 0 1 0 0  bbc
.b .. .a ..    |  0  4 |  0 0 0  0 2 0  2 | * * *  *  *  *  * 9 * * | 0 0 1 0 0 0 1 0  abab
.. .b .a ..    |  0  4 |  0 0 0  0 0 2  2 | * * *  *  *  *  * * 9 * | 0 0 0 0 1 0 0 1  abab
.. .. .a3.o    |  0  3 |  0 0 0  0 0 0  3 | * * *  *  *  *  * * * 6 | 0 0 0 0 0 0 1 1  aaa
---------------+-------+------------------+-------------------------+----------------
a.3o. b. ..    |  6  0 |  6 3 0  0 0 0  0 | 2 3 0  0  0  0  0 0 0 0 | 3 * * * * * * *  (a,b)-trip
a.3o. .. b.    |  6  0 |  6 0 3  0 0 0  0 | 2 0 3  0  0  0  0 0 0 0 | * 3 * * * * * *  (a,b)-trip
ab .. ba ..&#c |  4  4 |  2 2 0  4 2 0  2 | 0 1 0  2  0  2  0 1 0 0 | * * 9 * * * * *  recta
ab .. .. bo&#c |  4  2 |  2 0 2  4 1 0  0 | 0 0 1  2  0  0  2 0 0 0 | * * * 9 * * * *  wedge
.. ob ba ..&#c |  2  4 |  0 1 0  4 0 2  2 | 0 0 0  0  2  2  0 0 1 0 | * * * * 9 * * *  wedge
.. ob .. bo&#c |  2  2 |  0 0 1  4 0 1  0 | 0 0 0  0  2  0  2 0 0 0 | * * * * * 9 * *  (b,c)-2ap
.b .. .a3.o    |  0  6 |  0 0 0  0 3 0  6 | 0 0 0  0  0  0  0 3 0 2 | * * * * * * 3 *  (a,b)-trip
.. .b .a3.o    |  0  6 |  0 0 0  0 0 3  6 | 0 0 0  0  0  0  0 0 3 2 | * * * * * * * 3  (a,b)-trip

or
o.3o. o.3o.    & | 36 |  2  1  1  2 |  1  2  2  4  3 | 1 1 2  3 1
-----------------+----+-------------+----------------+-----------
a. .. .. ..    & |  2 | 36  *  *  * |  1  1  1  1  0 | 1 1 1  1 0
.. .. b. ..    & |  2 |  * 18  *  * |  0  2  0  2  0 | 1 0 2  1 0
.. .. .. b.    & |  2 |  *  * 18  * |  0  0  2  0  2 | 0 1 0  2 1
oo3oo oo3oo&#c   |  2 |  *  *  * 36 |  0  0  0  2  2 | 0 0 1  2 1
-----------------+----+-------------+----------------+-----------
a.3o. .. ..    & |  3 |  3  0  0  0 | 12  *  *  *  * | 1 1 0  0 0
a. .. b. ..    & |  4 |  2  2  0  0 |  * 18  *  *  * | 1 0 1  0 0
a. .. .. b.    & |  4 |  2  0  2  0 |  *  * 18  *  * | 0 1 0  1 0
ab .. .. ..&#c & |  4 |  1  1  0  2 |  *  *  * 36  * | 0 0 1  1 0
.. ob .. ..&#c & |  3 |  0  0  1  2 |  *  *  *  * 36 | 0 0 0  1 1
-----------------+----+-------------+----------------+-----------
a.3o. b. ..    & |  6 |  6  3  0  0 |  2  3  0  0  0 | 6 * *  * *  (a,b)-trip
a.3o. .. b.    & |  6 |  6  0  3  0 |  2  0  3  0  0 | * 6 *  * *  (a,b)-trip
ab .. ba ..&#c   |  8 |  4  4  0  4 |  0  2  0  4  0 | * * 9  * *  recta
ab .. .. bo&#c & |  6 |  2  1  2  4 |  0  0  1  2  2 | * * * 18 *  wedge
.. ob .. bo&#c & |  4 |  0  0  2  4 |  0  0  0  0  4 | * * *  * 9  (b,c)-2ap

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