Acronym pecupe
Name pentagonal-cupola prism,
pentagonal-prism atop decagonal-prism
Segmentochoron display  
Circumradius sqrt(3+sqrt(5)) = 2.288246
Lace city
in approx. ASCII-art
x5o  x5x	-- pecu
        
        
x5o  x5x	-- pecu

 |    +- dip
 +------ pip
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer
more general:
n/d-cupe  
uniform relative:
sriddip  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

xx5ox xx&#x     → height = sqrt((5-sqrt(5))/10) = 0.525731
(pip || dip)

o.5o. o.    | 10  * |  2 1  2  0  0  0 | 1 2  2  1  2 0 0 0 | 1 1 2 1 0
.o5.o .o    |  * 20 |  0 0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------+-------+------------------+--------------------+----------
x. .. ..    |  2  0 | 10 *  *  *  *  * | 1 1  1  0  0 0 0 0 | 1 1 1 0 0
.. .. x.    |  2  0 |  * 5  *  *  *  * | 0 2  0  0  2 0 0 0 | 1 0 2 1 0
oo5oo oo&#x |  1  1 |  * * 20  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 |  * *  * 10  *  * | 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .x ..    |  0  2 |  * *  *  * 10  * | 0 0  0  1  0 1 0 1 | 0 1 0 1 1
.. .. .x    |  0  2 |  * *  *  *  * 10 | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------+-------+------------------+--------------------+----------
x.5o. ..    |  5  0 |  5 0  0  0  0  0 | 2 *  *  *  * * * * | 1 1 0 0 0
x. .. x.    |  4  0 |  2 2  0  0  0  0 | * 5  *  *  * * * * | 1 0 1 0 0
xx .. ..&#x |  2  2 |  1 0  2  1  0  0 | * * 10  *  * * * * | 0 1 1 0 0
.. ox ..&#x |  1  2 |  0 0  2  0  1  0 | * *  * 10  * * * * | 0 1 0 1 0
.. .. xx&#x |  2  2 |  0 1  2  0  0  1 | * *  *  * 10 * * * | 0 0 1 1 0
.x5.x ..    |  0 10 |  0 0  0  5  5  0 | * *  *  *  * 2 * * | 0 1 0 0 1
.x .. .x    |  0  4 |  0 0  0  2  0  2 | * *  *  *  * * 5 * | 0 0 1 0 1
.. .x .x    |  0  4 |  0 0  0  0  2  2 | * *  *  *  * * * 5 | 0 0 0 1 1
------------+-------+------------------+--------------------+----------
x.5o. x.     10  0 | 10 5  0  0  0  0 | 2 5  0  0  0 0 0 0 | 1 * * * *
xx5ox ..&#x   5 10 |  5 0 10  5  5  0 | 1 0  5  5  0 1 0 0 | * 2 * * *
xx .. xx&#x   4  4 |  2 2  4  2  0  2 | 0 1  2  0  2 0 1 0 | * * 5 * *
.. ox xx&#x   2  4 |  0 1  4  0  2  2 | 0 0  0  2  2 0 0 1 | * * * 5 *
.x5.x .x      0 20 |  0 0  0 10 10 10 | 0 0  0  0  0 2 5 5 | * * * * 1

xx5ox&#x || xx5ox&#x   → height = 1
(pecu || pecu)

o.5o.    || .. ..    | 5  * *  * | 2  2 1 0 0  0 0  0 0 0 | 1 2 1 2  2 0 0 0 0 0 0 0 | 1 1 2 1 0 0
.o5.o    || .. ..    | * 10 *  * | 0  1 0 1 1  1 0  0 0 0 | 0 1 1 0  1 1 1 1 0 0 0 0 | 1 0 1 1 1 0
.. ..    || o.5o.    | *  * 5  * | 0  0 1 0 0  0 2  2 0 0 | 0 0 0 2  2 0 0 0 1 2 1 0 | 0 1 2 1 0 1
.. ..    || .o5.o    | *  * * 10 | 0  0 0 0 0  1 0  1 1 1 | 0 0 0 0  1 0 1 1 0 1 1 1 | 0 0 1 1 1 1
---------------------+-----------+------------------------+--------------------------+------------
x. ..    || .. ..    | 2  0 0  0 | 5  * * * *  * *  * * * | 1 1 0 1  0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo5oo&#x || .. ..    | 1  1 0  0 | * 10 * *  * *  * * * * | 0 1 1 0  1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
o.5o.    || o.5o.    | 1  0 1  0 | *  * 5 * *  * *  * * * | 0 0 0 2  2 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.x ..    || .. ..    | 0  2 0  0 | *  * * 5 *  * *  * * * | 0 1 0 0  0 1 1 0 0 0 0 0 | 1 0 1 0 1 0
.. .x    || .. ..    | 0  2 0  0 | *  * * * 5  * *  * * * | 0 0 1 0  0 1 0 1 0 0 0 0 | 1 0 0 1 1 0
.o5.o    || .o5.o    | 0  1 0  1 | *  * * * * 10 *  * * * | 0 0 0 0  1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
.. ..    || x. ..    | 0  0 2  0 | *  * * * *  * 5  * * * | 0 0 0 1  0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.. ..    || oo5oo&#x | 0  0 1  1 | *  * * * *  * * 10 * * | 0 0 0 0  1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
.. ..    || .x ..    | 0  0 0  2 | *  * * * *  * *  * 5 * | 0 0 0 0  0 0 1 0 0 1 0 1 | 0 0 1 0 1 1
.. ..    || .. .x    | 0  0 0  2 | *  * * * *  * *  * * 5 | 0 0 0 0  0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------------+-----------+------------------------+--------------------------+------------
x.5o.    || .. ..    | 5  0 0  0 | 5  0 0 0 0  0 0  0 0 0 | 1 * * *  * * * * * * * * | 1 1 0 0 0 0
xx ..&#x || .. ..    | 2  2 0  0 | 1  2 0 1 0  0 0  0 0 0 | * 5 * *  * * * * * * * * | 1 0 1 0 0 0
.. ox&#x || .. ..    | 1  2 0  0 | 0  2 0 0 1  0 0  0 0 0 | * * 5 *  * * * * * * * * | 1 0 0 1 0 0
x. ..    || x. ..    | 2  0 2  0 | 1  0 2 0 0  0 1  0 0 0 | * * * 5  * * * * * * * * | 0 1 1 0 0 0
oo5oo&#x || oo5oo&#x | 1  1 1  1 | 0  1 1 0 0  1 0  1 0 0 | * * * * 10 * * * * * * * | 0 0 1 1 0 0
.x5.x    || .. ..    | 0 10 0  0 | 0  0 0 5 5  0 0  0 0 0 | * * * *  * 1 * * * * * * | 1 0 0 0 1 0
.x ..    || .x ..    | 0  2 0  2 | 0  0 0 1 0  2 0  0 1 0 | * * * *  * * 5 * * * * * | 0 0 1 0 1 0
.. .x    || .. .x    | 0  2 0  2 | 0  0 0 0 1  2 0  0 0 1 | * * * *  * * * 5 * * * * | 0 0 0 1 1 0
.. ..    || x.5o.    | 0  0 5  0 | 0  0 0 0 0  0 5  0 0 0 | * * * *  * * * * 1 * * * | 0 1 0 0 0 1
.. ..    || xx ..&#x | 0  0 2  2 | 0  0 0 0 0  0 1  2 1 0 | * * * *  * * * * * 5 * * | 0 0 1 0 0 1
.. ..    || .. ox&#x | 0  0 1  2 | 0  0 0 0 0  0 0  2 0 1 | * * * *  * * * * * * 5 * | 0 0 0 1 0 1
.. ..    || .x5.x    | 0  0 0 10 | 0  0 0 0 0  0 0  0 5 5 | * * * *  * * * * * * * 1 | 0 0 0 0 1 1
---------------------+-----------+------------------------+--------------------------+------------
xx5ox&#x || .. ..     5 10 0  0 | 5 10 0 5 5  0 0  0 0 0 | 1 5 5 0  0 1 0 0 0 0 0 0 | 1 * * * * *
x.5o.    || x.5o.     5  0 5  0 | 5  0 5 0 0  0 5  0 0 0 | 1 0 0 5  0 0 0 0 1 0 0 0 | * 1 * * * *
xx ..&#x || xx ..&#x  2  2 2  2 | 1  2 2 1 0  2 1  2 1 0 | 0 1 0 1  2 0 1 0 0 1 0 0 | * * 5 * * *
.. ox&#x || .. ox&#x  1  2 1  2 | 0  2 1 0 1  2 0  2 0 1 | 0 0 1 0  2 0 0 1 0 0 1 0 | * * * 5 * *
.x5.x    || .x5.x     0 10 0 10 | 0  0 0 5 5 10 0  0 5 5 | 0 0 0 0  0 1 5 5 0 0 0 1 | * * * * 1 *
.. ..    || xx5ox&#x  0  0 5 10 | 0  0 0 0 0  0 5 10 5 5 | 0 0 0 0  0 0 0 0 1 5 5 1 | * * * * * 1

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