Acronym oappip, K-4.65
Name octagonal-antiprism prism
Circumradius sqrt[(5-2 sqrt(2+sqrt[2]))/(8-4 sqrt(2+sqrt[2])) = 1.463603
Lace city
in approx. ASCII-art
x8o   x8o	-- x x8o (op)
         
         
o8x   o8x	-- x o8x (gyro op)

 |     |
 |     +-- s2s8s (oap)
 +-------- s2s8s (oap)
Confer
general antiprism-prisms:
n-appip  
general polytopal classes:
segmentochora  
External
links
hedrondude

Incidence matrix according to Dynkin symbol

x s2s8s

. demi( . . . ) | 32 |  1  1  1  2 | 1 1  2 1  3 | 1  3 1
----------------+----+-------------+-------------+-------
x demi( . . . ) |  2 | 16  *  *  * | 1 1  2 0  0 | 1  3 0
.       s2s .   |  2 |  * 16  *  * | 1 0  0 0  2 | 0  2 1
.       s 2 s   |  2 |  *  * 16  * | 0 1  0 0  2 | 0  2 1
. sefa( . s8s ) |  2 |  *  *  * 32 | 0 0  1 1  1 | 1  1 1
----------------+----+-------------+-------------+-------
x       s2s .   |  4 |  2  2  0  0 | 8 *  * *  * | 0  2 0
x       s 2 s   |  4 |  2  0  2  0 | * 8  * *  * | 0  2 0
x sefa( . s8s ) |  4 |  2  0  0  2 | * * 16 *  * | 1  1 0
.       . s8s     8 |  0  0  0  8 | * *  * 4  * | 1  0 1
. sefa( s2s8s ) |  3 |  0  1  1  1 | * *  * * 32 | 0  1 1
----------------+----+-------------+-------------+-------
x       . s8s    16 |  8  0  0 16 | 0 0  8 2  0 | 2  * *
x sefa( s2s8s )   6 |  3  2  2  2 | 1 1  1 0  2 | * 16 *
.       s2s8s    16 |  0  8  8 16 | 0 0  0 2 16 | *  * 2

xx xo8ox&#x   → height = sqrt[(1+sqrt(2+sqrt[2]))/(2+sqrt(2+sqrt[2]))] = 0.860296
(op || gyro op)

o. o.8o.    | 16  * | 1  2  2 0  0 | 2 1  2  2  1 0 0 | 1 2 1 1 0
.o .o8.o    |  * 16 | 0  0  2 1  2 | 0 0  2  1  2 2 1 | 0 1 2 1 1
------------+-------+--------------+------------------+----------
x. .. ..    |  2  0 | 8  *  * *  * | 2 0  2  0  0 0 0 | 1 2 1 0 0
.. x. ..    |  2  0 | * 16  * *  * | 1 1  0  1  0 0 0 | 1 1 0 1 0
oo oo8oo&#x |  1  1 | *  * 32 *  * | 0 0  1  1  1 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 | *  *  * 8  * | 0 0  2  0  0 2 0 | 0 1 2 0 1
.. .x ..    |  0  2 | *  *  * * 16 | 0 0  0  0  1 1 1 | 0 0 1 1 1
------------+-------+--------------+------------------+----------
x. x. ..    |  4  0 | 2  2  0 0  0 | 8 *  *  *  * * * | 1 1 0 0 0
.. x.8o.    |  8  0 | 0  8  0 0  0 | * 2  *  *  * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 16  *  * * * | 0 1 1 0 0
.. xo ..&#x |  2  1 | 0  1  2 0  0 | * *  * 16  * * * | 0 1 0 1 0
.. .. ox&#x |  1  2 | 0  0  2 0  1 | * *  *  * 16 * * | 0 0 1 1 0
.x .. .x    |  0  4 | 0  0  0 2  2 | * *  *  *  * 8 * | 0 0 1 0 1
.. .o8.x    |  0  8 | 0  0  0 0  8 | * *  *  *  * * 2 | 0 0 0 1 1
------------+-------+--------------+------------------+----------
x. x.8o.     16  0 | 8 16  0 0  0 | 8 2  0  0  0 0 0 | 1 * * * *
xx xo ..&#x   4  2 | 2  2  4 1  0 | 1 0  2  2  0 0 0 | * 8 * * *
xx .. ox&#x   2  4 | 1  0  4 2  2 | 0 0  2  0  2 1 0 | * * 8 * *
.. xo8ox&#x   8  8 | 0  8 16 0  8 | 0 1  0  8  8 0 1 | * * * 2 *
.x .o8.x      0 16 | 0  0  0 8 16 | 0 0  0  0  0 8 2 | * * * * 1

s2s8s || s2s8s   → height = 1
(oap || oap)

demi( . . . )                 | 16  * | 1 1  2  1 0 0  0 | 1  3 1 1  2 0  0 | 1 1  3 0
                demi( . . . ) |  * 16 | 0 0  0  1 1 1  2 | 0  0 1 1  2 1  3 | 0 1  3 1
------------------------------+-------+------------------+------------------+---------
      s2s .                   |  2  0 | 8 *  *  * * *  * | 0  2 1 0  0 0  0 | 1 0  1 0
      s 2 s                   |  2  0 | * 8  *  * * *  * | 0  2 0 1  0 0  0 | 1 0  1 0
sefa( . s8s )                 |  2  0 | * * 16  * * *  * | 1  1 0 0  1 0  0 | 1 1  1 0
demi( . . . ) || demi( . . . ) |  1  1 | * *  * 16 * *  * | 0  0 1 1  2 0  0 | 0 1  3 0
                      s2s .   |  0  2 | * *  *  * 8 *  * | 0  0 1 0  0 0  2 | 0 0  2 1
                      s 2 s   |  0  2 | * *  *  * * 8  * | 0  0 0 1  0 0  2 | 0 0  2 1
                sefa( . s8s ) |  0  2 | * *  *  * * * 16 | 0  0 0 0  1 1  1 | 0 1  1 1
------------------------------+-------+------------------+------------------+---------
      . s8s                     8  0 | 0 0  8  0 0 0  0 | 2  * * *  * *  * | 1 1  0 0
sefa( s2s8s )                 |  3  0 | 1 1  1  0 0 0  0 | * 16 * *  * *  * | 1 0  1 0
      s2s .   ||       s2s .   |  2  2 | 1 0  0  2 1 0  0 | *  * 8 *  * *  * | 0 0  2 0
      s 2 s   ||       s 2 s   |  2  2 | 0 1  0  2 0 1  0 | *  * * 8  * *  * | 0 0  2 0
sefa( . s8s ) || sefa( . s8s ) |  2  2 | 0 0  1  2 0 0  1 | *  * * * 16 *  * | 0 1  1 0
                      . s8s     0  8 | 0 0  0  0 0 0  8 | *  * * *  * 2  * | 0 1  0 1
                sefa( s2s8s ) |  0  3 | 0 0  0  0 1 1  1 | *  * * *  * * 16 | 0 0  1 1
------------------------------+-------+------------------+------------------+---------
      s2s8s                    16  0 | 8 8 16  0 0 0  0 | 2 16 0 0  0 0  0 | 1 *  * *
      . s8s   ||       . s8s     8  8 | 0 0  8  8 0 0  8 | 1  0 0 0  8 1  0 | * 2  * *
sefa( s2s8s ) || sefa( s2s8s )   3  3 | 1 1  1  3 1 1  1 | 0  1 1 1  1 0  1 | * * 16 *
                      s2s8s     0 16 | 0 0  0  0 8 8 16 | 0  0 0 0  0 2 16 | * *  * 1

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