Acronym dappip, K-4.96
Name decagonal-antiprism prism
Circumradius sqrt[(5-sqrt(10+2 sqrt[5]))/(8-2 sqrt(10+2 sqrt[5])) = 1.747560
Lace city
in approx. ASCII-art 
x10o   x10o	-- x x10o (dip)
           
           
o10x   o10x	-- x o10x (gyro dip)

 |      |
 |      +-- s2s10s (dap)
 +--------- s2s10s (dap)
Face vector 40, 100, 84, 24
Confer
general antiprism-prisms:
n-appip  
general polytopal classes:
segmentochora  
External
links 		hedrondude   wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

x s2s10s

. demi( . .  . ) | 40 |  1  1  1  2 |  1  1  2 1  3 | 1  3 1
-----------------+----+-------------+---------------+-------
x demi( . .  . ) |  2 | 20  *  *  * |  1  1  2 0  0 | 1  3 0
.       s2s  .   |  2 |  * 20  *  * |  1  0  0 0  2 | 0  2 1
.       s 2  s   |  2 |  *  * 20  * |  0  1  0 0  2 | 0  2 1
. sefa( . s10s ) |  2 |  *  *  * 40 |  0  0  1 1  1 | 1  1 1
-----------------+----+-------------+---------------+-------
x       s2s  .   |  4 |  2  2  0  0 | 10  *  * *  * | 0  2 0
x       s 2  s   |  4 |  2  0  2  0 |  * 10  * *  * | 0  2 0
x sefa( . s10s ) |  4 |  2  0  0  2 |  *  * 20 *  * | 1  1 0
.       . s10s   ♦ 10 |  0  0  0 10 |  *  *  * 4  * | 1  0 1
. sefa( s2s10s ) |  3 |  0  1  1  1 |  *  *  * * 40 | 0  1 1
-----------------+----+-------------+---------------+-------
x       . s10s   ♦ 20 | 10  0  0 20 |  0  0 10 2  0 | 2  * *
x sefa( s2s10s ) ♦  6 |  3  2  2  2 |  1  1  1 0  2 | * 20 *
.       s2s10s   ♦ 20 |  0 10 10 20 |  0  0  0 2 20 | *  * 2


xx xo10ox&#x   → height = sqrt[(2+sqrt(10+2 sqrt[5]))/(4+sqrt(10+2 sqrt[5]))] = 0.862397
(dip || gyro dip)

o. o.10o.    | 20  * |  1  2  2  0  0 |  2 1  2  2  1  0 0 | 1  2  1 1 0
.o .o10.o    |  * 20 |  0  0  2  1  2 |  0 0  2  1  2  2 1 | 0  1  2 1 1
-------------+-------+----------------+--------------------+------------
x. ..  ..    |  2  0 | 10  *  *  *  * |  2 0  2  0  0  0 0 | 1  2  1 0 0
.. x.  ..    |  2  0 |  * 20  *  *  * |  1 1  0  1  0  0 0 | 1  1  0 1 0
oo oo10oo&#x |  1  1 |  *  * 40  *  * |  0 0  1  1  1  0 0 | 0  1  1 1 0
.x ..  ..    |  0  2 |  *  *  * 10  * |  0 0  2  0  0  2 0 | 0  1  2 0 1
.. .x  ..    |  0  2 |  *  *  *  * 20 |  0 0  0  0  1  1 1 | 0  0  1 1 1
-------------+-------+----------------+--------------------+------------
x. x.  ..    |  4  0 |  2  2  0  0  0 | 10 *  *  *  *  * * | 1  1  0 0 0
.. x.10o.    | 10  0 |  0 10  0  0  0 |  * 2  *  *  *  * * | 1  0  0 1 0
xx ..  ..&#x |  2  2 |  1  0  2  1  0 |  * * 20  *  *  * * | 0  1  1 0 0
.. xo  ..&#x |  2  1 |  0  1  2  0  0 |  * *  * 20  *  * * | 0  1  0 1 0
.. ..  ox&#x |  1  2 |  0  0  2  0  1 |  * *  *  * 20  * * | 0  0  1 1 0
.x ..  .x    |  0  4 |  0  0  0  2  2 |  * *  *  *  * 10 * | 0  0  1 0 1
.. .o10.x    |  0 10 |  0  0  0  0 10 |  * *  *  *  *  * 2 | 0  0  0 1 1
-------------+-------+----------------+--------------------+------------
x. x.10o.    ♦ 20  0 | 10 20  0  0  0 | 10 2  0  0  0  0 0 | 1  *  * * *
xx xo  ..&#x ♦  4  2 |  2  2  4  1  0 |  1 0  2  2  0  0 0 | * 10  * * *
xx ..  ox&#x ♦  2  4 |  1  0  4  2  2 |  0 0  2  0  2  1 0 | *  * 10 * *
.. xo10ox&#x ♦ 10 10 |  0 10 20  0 10 |  0 1  0 10 10  0 1 | *  *  * 2 *
.x .o10.x    ♦  0 20 |  0  0  0 10 20 |  0 0  0  0  0 10 2 | *  *  * * 1


s2s10s || s2s10s   → height = 1
(dap || dap)

demi( . .  . )                  | 20  * |  1  1  2  1  0  0  0 | 1  3  1  1  2 0  0 | 1 1  3 0
                 demi( . .  . ) |  * 20 |  0  0  0  1  1  1  2 | 0  0  1  1  2 1  3 | 0 1  3 1
--------------------------------+-------+----------------------+--------------------+---------
      s2s  .                    |  2  0 | 10  *  *  *  *  *  * | 0  2  1  0  0 0  0 | 1 0  1 0
      s 2  s                    |  2  0 |  * 10  *  *  *  *  * | 0  2  0  1  0 0  0 | 1 0  1 0
sefa( . s10s )                  |  2  0 |  *  * 20  *  *  *  * | 1  1  0  0  1 0  0 | 1 1  1 0
demi( . .  . ) || demi( . .  . ) |  1  1 |  *  *  * 20  *  *  * | 0  0  1  1  2 0  0 | 0 1  3 0
                       s2s  .   |  0  2 |  *  *  *  * 10  *  * | 0  0  1  0  0 0  2 | 0 0  2 1
                       s 2  s   |  0  2 |  *  *  *  *  * 10  * | 0  0  0  1  0 0  2 | 0 0  2 1
                 sefa( . s10s ) |  0  2 |  *  *  *  *  *  * 20 | 0  0  0  0  1 1  1 | 0 1  1 1
--------------------------------+-------+----------------------+--------------------+---------
      . s10s                    ♦ 10  0 |  0  0 10  0  0  0  0 | 2  *  *  *  * *  * | 1 1  0 0
sefa( s2s10s )                  |  3  0 |  1  1  1  0  0  0  0 | * 20  *  *  * *  * | 1 0  1 0
      s2s  .   ||       s2s  .   |  2  2 |  1  0  0  2  1  0  0 | *  * 10  *  * *  * | 0 0  2 0
      s 2  s   ||       s 2  s   |  2  2 |  0  1  0  2  0  1  0 | *  *  * 10  * *  * | 0 0  2 0
sefa( . s10s ) || sefa( . s10s ) |  2  2 |  0  0  1  2  0  0  1 | *  *  *  * 20 *  * | 0 1  1 0
                       . s10s   ♦  0 10 |  0  0  0  0  0  0 10 | *  *  *  *  * 2  * | 0 1  0 1
                 sefa( s2s10s ) |  0  3 |  0  0  0  0  1  1  1 | *  *  *  *  * * 20 | 0 0  1 1
--------------------------------+-------+----------------------+--------------------+---------
      s2s10s                    ♦ 20  0 | 10 10 20  0  0  0  0 | 2 20  0  0  0 0  0 | 1 *  * *
      . s10s   ||       . s10s   ♦ 10 10 |  0  0 10 10  0  0 10 | 1  0  0  0 10 1  0 | * 2  * *
sefa( s2s10s ) || sefa( s2s10s ) ♦  3  3 |  1  1  1  3  1  1  1 | 0  1  1  1  1 0  1 | * * 20 *
                       s2s10s   ♦  0 20 |  0  0  0  0 10 10 20 | 0  0  0  0  0 2 20 | * *  * 1

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