Acronym happip, K-4.53
Name hexagonal-antiprism prism
Circumradius sqrt[4+sqrt(3)]/2 = 1.197085
Lace city
in approx. ASCII-art
x6o   x6o	-- x x6o (hip)
         
         
o6x   o6x	-- x o6x (gyro hip)

 |     |
 |     +-- s2s6s (hap)
 +-------- s2s6s (hap)
Confer
general antiprism-prisms:
n-appip  
general polytopal classes:
segmentochora  
External
links
hedrondude

Incidence matrix according to Dynkin symbol

x s2s6s

. demi( . . . ) | 24 |  1  1  1  2 | 1 1  2 1  3 | 1  3 1
----------------+----+-------------+-------------+-------
x demi( . . . ) |  2 | 12  *  *  * | 1 1  2 0  0 | 1  3 0
.       s2s .   |  2 |  * 12  *  * | 1 0  0 0  2 | 0  2 1
.       s 2 s   |  2 |  *  * 12  * | 0 1  0 0  2 | 0  2 1
. sefa( . s6s ) |  2 |  *  *  * 24 | 0 0  1 1  1 | 1  1 1
----------------+----+-------------+-------------+-------
x       s2s .   |  4 |  2  2  0  0 | 6 *  * *  * | 0  2 0
x       s 2 s   |  4 |  2  0  2  0 | * 6  * *  * | 0  2 0
x sefa( . s6s ) |  4 |  2  0  0  2 | * * 12 *  * | 1  1 0
.       . s6s     6 |  0  0  0  6 | * *  * 4  * | 1  0 1
. sefa( s2s6s ) |  3 |  0  1  1  1 | * *  * * 24 | 0  1 1
----------------+----+-------------+-------------+-------
x       . s6s    12 |  6  0  0 12 | 0 0  6 2  0 | 2  * *
x sefa( s2s6s )   6 |  3  2  2  2 | 1 1  1 0  2 | * 12 *
.       s2s6s    12 |  0  6  6 12 | 0 0  0 2 12 | *  * 2

x s2s12o

. demi( . .  . ) | 24 |  1  2  2 |  2  2 1  3 | 1  3 1
-----------------+----+----------+------------+-------
x demi( . .  . ) |  2 | 12  *  * |  2  2 0  0 | 1  3 0
.       s2s  .   |  2 |  * 24  * |  1  0 0  2 | 0  2 1
. sefa( . s12o ) |  2 |  *  * 24 |  0  1 1  1 | 1  1 1
-----------------+----+----------+------------+-------
x       s2s  .   |  4 |  2  2  0 | 12  * *  * | 0  2 0
x sefa( . s12o ) |  4 |  2  0  2 |  * 12 *  * | 1  1 0
.       . s12o     6 |  0  0  6 |  *  * 4  * | 1  0 1
. sefa( s2s12o ) |  3 |  0  2  1 |  *  * * 24 | 0  1 1
-----------------+----+----------+------------+-------
x       . s12o    12 |  6  0 12 |  0  6 2  0 | 2  * *
x sefa( s2s12o )   6 |  3  4  2 |  2  1 0  2 | * 12 *
.       s2s12o    12 |  0 12 12 |  0  0 2 12 | *  * 2

xx xo6ox&#x   → height = sqrt[sqrt(3)-1] = 0.855600
(hip || gyro hip)

o. o.6o.    | 12  * | 1  2  2 0  0 | 2 1  2  2  1 0 0 | 1 2 1 1 0
.o .o6.o    |  * 12 | 0  0  2 1  2 | 0 0  2  1  2 2 1 | 0 1 2 1 1
------------+-------+--------------+------------------+----------
x. .. ..    |  2  0 | 6  *  * *  * | 2 0  2  0  0 0 0 | 1 2 1 0 0
.. x. ..    |  2  0 | * 12  * *  * | 1 1  0  1  0 0 0 | 1 1 0 1 0
oo oo6oo&#x |  1  1 | *  * 24 *  * | 0 0  1  1  1 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 | *  *  * 6  * | 0 0  2  0  0 2 0 | 0 1 2 0 1
.. .x ..    |  0  2 | *  *  * * 12 | 0 0  0  0  1 1 1 | 0 0 1 1 1
------------+-------+--------------+------------------+----------
x. x. ..    |  4  0 | 2  2  0 0  0 | 6 *  *  *  * * * | 1 1 0 0 0
.. x.6o.    |  6  0 | 0  6  0 0  0 | * 2  *  *  * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 12  *  * * * | 0 1 1 0 0
.. xo ..&#x |  2  1 | 0  1  2 0  0 | * *  * 12  * * * | 0 1 0 1 0
.. .. ox&#x |  1  2 | 0  0  2 0  1 | * *  *  * 12 * * | 0 0 1 1 0
.x .. .x    |  0  4 | 0  0  0 2  2 | * *  *  *  * 6 * | 0 0 1 0 1
.. .o6.x    |  0  6 | 0  0  0 0  6 | * *  *  *  * * 2 | 0 0 0 1 1
------------+-------+--------------+------------------+----------
x. x.6o.     12  0 | 6 12  0 0  0 | 6 2  0  0  0 0 0 | 1 * * * *
xx xo ..&#x   4  2 | 2  2  4 1  0 | 1 0  2  2  0 0 0 | * 6 * * *
xx .. ox&#x   2  4 | 1  0  4 2  2 | 0 0  2  0  2 1 0 | * * 6 * *
.. xo6ox&#x   6  6 | 0  6 12 0  6 | 0 1  0  6  6 0 1 | * * * 2 *
.x .o6.x      0 12 | 0  0  0 6 12 | 0 0  0  0  0 6 2 | * * * * 1

s2s6s || s2s6s   → height = 1
(hap || hap)

demi( . . . )                 | 12  * | 1 1  2  1 0 0  0 | 1  3 1 1  2 0  0 | 1 1  3 0
                demi( . . . ) |  * 12 | 0 0  0  1 1 1  2 | 0  0 1 1  2 1  3 | 0 1  3 1
------------------------------+-------+------------------+------------------+---------
      s2s .                   |  2  0 | 6 *  *  * * *  * | 0  2 1 0  0 0  0 | 1 0  1 0
      s 2 s                   |  2  0 | * 6  *  * * *  * | 0  2 0 1  0 0  0 | 1 0  1 0
sefa( . s6s )                 |  2  0 | * * 12  * * *  * | 1  1 0 0  1 0  0 | 1 1  1 0
demi( . . . ) || demi( . . . ) |  1  1 | * *  * 12 * *  * | 0  0 1 1  2 0  0 | 0 1  3 0
                      s2s .   |  0  2 | * *  *  * 6 *  * | 0  0 1 0  0 0  2 | 0 0  2 1
                      s 2 s   |  0  2 | * *  *  * * 6  * | 0  0 0 1  0 0  2 | 0 0  2 1
                sefa( . s6s ) |  0  2 | * *  *  * * * 12 | 0  0 0 0  1 1  1 | 0 1  1 1
------------------------------+-------+------------------+------------------+---------
      . s6s                     6  0 | 0 0  6  0 0 0  0 | 2  * * *  * *  * | 1 1  0 0
sefa( s2s6s )                 |  3  0 | 1 1  1  0 0 0  0 | * 12 * *  * *  * | 1 0  1 0
      s2s .   ||       s2s .   |  2  2 | 1 0  0  2 1 0  0 | *  * 6 *  * *  * | 0 0  2 0
      s 2 s   ||       s 2 s   |  2  2 | 0 1  0  2 0 1  0 | *  * * 6  * *  * | 0 0  2 0
sefa( . s6s ) || sefa( . s6s ) |  2  2 | 0 0  1  2 0 0  1 | *  * * * 12 *  * | 0 1  1 0
                      . s6s     0  6 | 0 0  0  0 0 0  6 | *  * * *  * 2  * | 0 1  0 1
                sefa( s2s6s ) |  0  3 | 0 0  0  0 1 1  1 | *  * * *  * * 12 | 0 0  1 1
------------------------------+-------+------------------+------------------+---------
      s2s6s                    12  0 | 6 6 12  0 0 0  0 | 2 12 0 0  0 0  0 | 1 *  * *
      . s6s   ||       . s6s     6  6 | 0 0  6  6 0 0  6 | 1  0 0 0  6 1  0 | * 2  * *
sefa( s2s6s ) || sefa( s2s6s )   3  3 | 1 1  1  3 1 1  1 | 0  1 1 1  1 0  1 | * * 12 *
                      s2s6s     0 12 | 0 0  0  0 6 6 12 | 0  0 0 0  0 2 12 | * *  * 1

s2s12o || s2s12o   → height = 1
(hap || hap)

demi( . .  . )                  | 12  * |  2  2  1  0  0 | 1  3  2  2 0  0 | 1 1  3 0
                 demi( . .  . ) |  * 12 |  0  0  1  2  2 | 0  0  2  2 1  3 | 0 1  3 1
--------------------------------+-------+----------------+-----------------+---------
      s2s  .                    |  2  0 | 12  *  *  *  * | 0  2  1  0 0  0 | 1 0  2 0
sefa( . s12o )                  |  2  0 |  * 12  *  *  * | 1  1  0  1 0  0 | 1 1  1 0
demi( . .  . ) || demi( . .  . ) |  1  1 |  *  * 12  *  * | 0  0  2  2 0  0 | 0 1  3 0
                       s2s  . ) |  0  2 |  *  *  * 12  * | 0  0  1  0 0  2 | 0 0  2 1
                 sefa( . s12o ) |  0  2 |  *  *  *  * 12 | 0  0  0  1 1  1 | 0 1  1 1
--------------------------------+-------+----------------+-----------------+---------
      . s12o                      6  0 |  0  6  0  0  0 | 2  *  *  * *  * | 1 1  0 0
sefa( s2s12o )                  |  3  0 |  2  1  0  0  0 | * 12  *  * *  * | 1 0  1 0
      s2s  . ) ||       s2s  . ) |  2  2 |  1  0  2  1  0 | *  * 12  * *  * | 0 0  2 0
sefa( . s12o ) || sefa( . s12o ) |  2  2 |  0  1  2  0  1 | *  *  * 12 *  * | 0 1  1 0
                       . s12o     0  6 |  0  0  0  0  6 | *  *  *  * 2  * | 0 1  0 1
                 sefa( s2s12o ) |  0  3 |  0  0  0  2  1 | *  *  *  * * 12 | 0 0  1 1
--------------------------------+-------+----------------+-----------------+---------
      s2s12o                     12  0 | 12 12  0  0  0 | 2 12  0  0 0  0 | 1 *  * *
      . s12o   ||       . s12o     6  6 |  0  6  6  0  6 | 1  0  0  6 1  0 | * 2  * *
sefa( s2s12o ) || sefa( s2s12o )   3  3 |  2  1  3  2  1 | 0  1  2  1 0  1 | * * 12 *
                       s2s12o     0 12 |  0  0  0 12 12 | 0  0  0  0 2 12 | * *  * 1

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