Acronym pappip, K-4.39
Name pentagonal-antiprism prism
Segmentochoron display  
Circumradius sqrt[(7+sqrt(5))/8] = 1.074481
Lace city
in approx. ASCII-art 
x5o   x5o	-- x x5o (pip)
         
         
o5x   o5x	-- x o5x (gyro pip)

 |     |
 |     +-- s2s5s (pap)
 +-------- s2s5s (pap)
Dihedral angles
  • at {4} between trip and trip:   arccos(-sqrt(5)/3) = 138.189685°
  • at {4} between pip and trip:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
  • at {3} between pap and trip:   90°
  • at {5} between pap and pip:   90°
Face vector 20, 50, 44, 14
Confer
general antiprism-prisms:
n-appip  
general polytopal classes:
segmentochora  
External
links 		hedrondude   wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

x s2s5s

. demi( . . . ) | 20 |  1  1  1  2 | 1 1  2 1  3 | 1  3 1
----------------+----+-------------+-------------+-------
x demi( . . . ) |  2 | 10  *  *  * | 1 1  2 0  0 | 1  3 0
.       s2s .   |  2 |  * 10  *  * | 1 0  0 0  2 | 0  2 1
.       s 2 s   |  2 |  *  * 10  * | 0 1  0 0  2 | 0  2 1
. sefa( . s5s ) |  2 |  *  *  * 20 | 0 0  1 1  1 | 1  1 1
----------------+----+-------------+-------------+-------
x       s2s .   |  4 |  2  2  0  0 | 5 *  * *  * | 0  2 0
x       s 2 s   |  4 |  2  0  2  0 | * 5  * *  * | 0  2 0
x sefa( . s5s ) |  4 |  2  0  0  2 | * * 10 *  * | 1  1 0
.       . s5s   ♦  5 |  0  0  0  5 | * *  * 4  * | 1  0 1
. sefa( s2s5s ) |  3 |  0  1  1  1 | * *  * * 20 | 0  1 1
----------------+----+-------------+-------------+-------
x       . s5s   ♦ 10 |  5  0  0 10 | 0 0  5 2  0 | 2  * *
x sefa( s2s5s ) ♦  6 |  3  2  2  2 | 1 1  1 0  2 | * 10 *
.       s2s5s   ♦ 10 |  0  5  5 10 | 0 0  0 2 10 | *  * 2


x s2s10o

. demi( . .  . ) | 20 |  1  2  2 |  2  2 1  3 | 1  3 1
-----------------+----+----------+------------+-------
x demi( . .  . ) |  2 | 10  *  * |  2  2 0  0 | 1  3 0
.       s2s  .   |  2 |  * 20  * |  1  0 0  2 | 0  2 1
. sefa( . s10o ) |  2 |  *  * 20 |  0  1 1  1 | 1  1 1
-----------------+----+----------+------------+-------
x       s2s  .   |  4 |  2  2  0 | 10  * *  * | 0  2 0
x sefa( . s10o ) |  4 |  2  0  2 |  * 10 *  * | 1  1 0
.       . s10o   ♦  5 |  0  0  5 |  *  * 4  * | 1  0 1
. sefa( s2s10o ) |  3 |  0  2  1 |  *  * * 20 | 0  1 1
-----------------+----+----------+------------+-------
x       . s10o   ♦ 10 |  5  0 10 |  0  5 2  0 | 2  * *
x sefa( s2s10o ) ♦  6 |  3  4  2 |  2  1 0  2 | * 10 *
.       s2s10o   ♦ 10 |  0 10 10 |  0  0 2 10 | *  * 2


xx xo5ox&#x   → height = sqrt((5+sqrt(5))/10) = 0.850651
(pip || gyro pip)

o. o.5o.    | 10  * | 1  2  2 0  0 | 2 1  2  2  1 0 0 | 1 2 1 1 0
.o .o5.o    |  * 10 | 0  0  2 1  2 | 0 0  2  1  2 2 1 | 0 1 2 1 1
------------+-------+--------------+------------------+----------
x. .. ..    |  2  0 | 5  *  * *  * | 2 0  2  0  0 0 0 | 1 2 1 0 0
.. x. ..    |  2  0 | * 10  * *  * | 1 1  0  1  0 0 0 | 1 1 0 1 0
oo oo5oo&#x |  1  1 | *  * 20 *  * | 0 0  1  1  1 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 | *  *  * 5  * | 0 0  2  0  0 2 0 | 0 1 2 0 1
.. .x ..    |  0  2 | *  *  * * 10 | 0 0  0  0  1 1 1 | 0 0 1 1 1
------------+-------+--------------+------------------+----------
x. x. ..    |  4  0 | 2  2  0 0  0 | 5 *  *  *  * * * | 1 1 0 0 0
.. x.5o.    |  5  0 | 0  5  0 0  0 | * 2  *  *  * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 10  *  * * * | 0 1 1 0 0
.. xo ..&#x |  2  1 | 0  1  2 0  0 | * *  * 10  * * * | 0 1 0 1 0
.. .. ox&#x |  1  2 | 0  0  2 0  1 | * *  *  * 10 * * | 0 0 1 1 0
.x .. .x    |  0  4 | 0  0  0 2  2 | * *  *  *  * 5 * | 0 0 1 0 1
.. .o5.x    |  0  5 | 0  0  0 0  5 | * *  *  *  * * 2 | 0 0 0 1 1
------------+-------+--------------+------------------+----------
x. x.5o.    ♦ 10  0 | 5 10  0 0  0 | 5 2  0  0  0 0 0 | 1 * * * *
xx xo ..&#x ♦  4  2 | 2  2  4 1  0 | 1 0  2  2  0 0 0 | * 5 * * *
xx .. ox&#x ♦  2  4 | 1  0  4 2  2 | 0 0  2  0  2 1 0 | * * 5 * *
.. xo5ox&#x ♦  5  5 | 0  5 10 0  5 | 0 1  0  5  5 0 1 | * * * 2 *
.x .o5.x    ♦  0 10 | 0  0  0 5 10 | 0 0  0  0  0 5 2 | * * * * 1


s2s5s || s2s5s   → height = 1
(pap || pap)

demi( . . . )                 | 10  * | 1 1  2  1 0 0  0 | 1  3 1 1  2 0  0 | 1 1  3 0
                demi( . . . ) |  * 10 | 0 0  0  1 1 1  2 | 0  0 1 1  2 1  3 | 0 1  3 1
------------------------------+-------+------------------+------------------+---------
      s2s .                   |  2  0 | 5 *  *  * * *  * | 0  2 1 0  0 0  0 | 1 0  1 0
      s 2 s                   |  2  0 | * 5  *  * * *  * | 0  2 0 1  0 0  0 | 1 0  1 0
sefa( . s5s )                 |  2  0 | * * 10  * * *  * | 1  1 0 0  1 0  0 | 1 1  1 0
demi( . . . ) || demi( . . . ) |  1  1 | * *  * 10 * *  * | 0  0 1 1  2 0  0 | 0 1  3 0
                      s2s .   |  0  2 | * *  *  * 5 *  * | 0  0 1 0  0 0  2 | 0 0  2 1
                      s 2 s   |  0  2 | * *  *  * * 5  * | 0  0 0 1  0 0  2 | 0 0  2 1
                sefa( . s5s ) |  0  2 | * *  *  * * * 10 | 0  0 0 0  1 1  1 | 0 1  1 1
------------------------------+-------+------------------+------------------+---------
      . s5s                   ♦  5  0 | 0 0  5  0 0 0  0 | 2  * * *  * *  * | 1 1  0 0
sefa( s2s5s )                 |  3  0 | 1 1  1  0 0 0  0 | * 10 * *  * *  * | 1 0  1 0
      s2s .   ||       s2s .   |  2  2 | 1 0  0  2 1 0  0 | *  * 5 *  * *  * | 0 0  2 0
      s 2 s   ||       s 2 s   |  2  2 | 0 1  0  2 0 1  0 | *  * * 5  * *  * | 0 0  2 0
sefa( . s5s ) || sefa( . s5s ) |  2  2 | 0 0  1  2 0 0  1 | *  * * * 10 *  * | 0 1  1 0
                      . s5s   ♦  0  5 | 0 0  0  0 0 0  5 | *  * * *  * 2  * | 0 1  0 1
                sefa( s2s5s ) |  0  3 | 0 0  0  0 1 1  1 | *  * * *  * * 10 | 0 0  1 1
------------------------------+-------+------------------+------------------+---------
      s2s5s                   ♦ 10  0 | 5 5 10  0 0 0  0 | 2 10 0 0  0 0  0 | 1 *  * *
      . s5s   ||       . s5s   ♦  5  5 | 0 0  5  5 0 0  5 | 1  0 0 0  5 1  0 | * 2  * *
sefa( s2s5s ) || sefa( s2s5s ) ♦  3  3 | 1 1  1  3 1 1  1 | 0  1 1 1  1 0  1 | * * 10 *
                      s2s5s   ♦  0 10 | 0 0  0  0 5 5 10 | 0  0 0 0  0 2 10 | * *  * 1


s2s10o || s2s10o   → height = 1
(pap || pap)

demi( . .  . )                  | 10  * |  2  2  1  0  0 | 1  3  2  2 0  0 | 1 1  3 0
                 demi( . .  . ) |  * 10 |  0  0  1  2  2 | 0  0  2  2 1  3 | 0 1  3 1
--------------------------------+-------+----------------+-----------------+---------
      s2s  .                    |  2  0 | 10  *  *  *  * | 0  2  1  0 0  0 | 1 0  2 0
sefa( . s10o )                  |  2  0 |  * 10  *  *  * | 1  1  0  1 0  0 | 1 1  1 0
demi( . .  . ) || demi( . .  . ) |  1  1 |  *  * 10  *  * | 0  0  2  2 0  0 | 0 1  3 0
                       s2s  . ) |  0  2 |  *  *  * 10  * | 0  0  1  0 0  2 | 0 0  2 1
                 sefa( . s10o ) |  0  2 |  *  *  *  * 10 | 0  0  0  1 1  1 | 0 1  1 1
--------------------------------+-------+----------------+-----------------+---------
      . s10o                    ♦  5  0 |  0  5  0  0  0 | 2  *  *  * *  * | 1 1  0 0
sefa( s2s10o )                  |  3  0 |  2  1  0  0  0 | * 10  *  * *  * | 1 0  1 0
      s2s  . ) ||       s2s  . ) |  2  2 |  1  0  2  1  0 | *  * 10  * *  * | 0 0  2 0
sefa( . s10o ) || sefa( . s10o ) |  2  2 |  0  1  2  0  1 | *  *  * 10 *  * | 0 1  1 0
                       . s10o   ♦  0  5 |  0  0  0  0  5 | *  *  *  * 2  * | 0 1  0 1
                 sefa( s2s10o ) |  0  3 |  0  0  0  2  1 | *  *  *  * * 10 | 0 0  1 1
--------------------------------+-------+----------------+-----------------+---------
      s2s10o                    ♦ 10  0 | 10 10  0  0  0 | 2 10  0  0 0  0 | 1 *  * *
      . s10o   ||       . s10o   ♦  5  5 |  0  5  5  0  5 | 1  0  0  5 1  0 | * 2  * *
sefa( s2s10o ) || sefa( s2s10o ) ♦  3  3 |  2  1  3  2  1 | 0  1  2  1 0  1 | * * 10 *
                       s2s10o   ♦  0 10 |  0  0  0 10 10 | 0  0  0  0 2 10 | * *  * 1

© 2004-2024
top of page