Acronym squappip, K-4.19
Name square-antiprism prism
Segmentochoron display  
Circumradius sqrt[(6+sqrt(2))/8] = 0.962692
Lace city
in approx. ASCII-art
x4o   x4o	-- x x4o (cube)
         
         
o4x   o4x	-- x o4x (gyro cube)

 |     |
 |     +-- s2s4s (squap)
 +-------- s2s4s (squap)
Dihedral angles
  • at {4} between trip and trip:   arccos[(1-2 sqrt(2))/3] = 127.551603°
  • at {4} between cube and trip:   arccos[(1-sqrt(2))/sqrt(3)] = 103.836160°
  • at {4} between cube and squap:   90°
  • at {3} between squap and trip:   90°
Confer
general antiprism-prisms:
n-appip  
general polytopal classes:
segmentochora  
External
links
hedrondude

Incidence matrix according to Dynkin symbol

x s2s4s

. demi( . . . ) | 16 | 1 1 1  2 | 1 1 2 1  3 | 1 3 1
----------------+----+----------+------------+------
x demi( . . . ) |  2 | 8 * *  * | 1 1 2 0  0 | 1 3 0
.       s2s .   |  2 | * 8 *  * | 1 0 0 0  2 | 0 2 1
.       s 2 s   |  2 | * * 8  * | 0 1 0 0  2 | 0 2 1
. sefa( . s4s ) |  2 | * * * 16 | 0 0 1 1  1 | 1 1 1
----------------+----+----------+------------+------
x       s2s .   |  4 | 2 2 0  0 | 4 * * *  * | 0 2 0
x       s 2 s   |  4 | 2 0 2  0 | * 4 * *  * | 0 2 0
x sefa( . s4s ) |  4 | 2 0 0  2 | * * 8 *  * | 1 1 0
.       . s4s     4 | 0 0 0  4 | * * * 4  * | 1 0 1
. sefa( s2s4s ) |  3 | 0 1 1  1 | * * * * 16 | 0 1 1
----------------+----+----------+------------+------
x       . s4s     8 | 4 0 0  8 | 0 0 4 2  0 | 2 * *
x sefa( s2s4s )   6 | 3 2 2  2 | 1 1 1 0  2 | * 8 *
.       s2s4s     8 | 0 4 4  8 | 0 0 0 2  8 | * * 2

x s2s8o

. demi( . . . ) | 16 | 1  2  2 | 2 2 1  3 | 1 3 1
----------------+----+---------+----------+------
x demi( . . . ) |  2 | 8  *  * | 2 2 0  0 | 1 3 0
.       s2s .   |  2 | * 16  * | 1 0 0  2 | 0 2 1
. sefa( . s8o ) |  2 | *  * 16 | 0 1 1  1 | 1 1 1
----------------+----+---------+----------+------
x       s2s .   |  4 | 2  2  0 | 8 * *  * | 0 2 0
x sefa( . s8o ) |  4 | 2  0  2 | * 8 *  * | 1 1 0
.       . s8o     4 | 0  0  4 | * * 4  * | 1 0 1
. sefa( s2s8o ) |  3 | 0  2  1 | * * * 16 | 0 1 1
----------------+----+---------+----------+------
x       . s8o     8 | 4  0  8 | 0 4 2  0 | 2 * *
x sefa( s2s8o )   6 | 3  4  2 | 2 1 0  2 | * 8 *
.       s2s8o     8 | 0  8  8 | 0 0 2  8 | * * 2

xx xo4ox&#x   → height = 1/sqrt(sqrt(2)) = 0.840896
(cube || gyro cube)

o. o.4o.    | 8 * | 1 2  2 0 0 | 2 1 2 2 1 0 0 | 1 2 1 1 0
.o .o4.o    | * 8 | 0 0  2 1 2 | 0 0 2 1 2 2 1 | 0 1 2 1 1
------------+-----+------------+---------------+----------
x. .. ..    | 2 0 | 4 *  * * * | 2 0 2 0 0 0 0 | 1 2 1 0 0
.. x. ..    | 2 0 | * 8  * * * | 1 1 0 1 0 0 0 | 1 1 0 1 0
oo oo4oo&#x | 1 1 | * * 16 * * | 0 0 1 1 1 0 0 | 0 1 1 1 0
.x .. ..    | 0 2 | * *  * 4 * | 0 0 2 0 0 2 0 | 0 1 2 0 1
.. .x ..    | 0 2 | * *  * * 8 | 0 0 0 0 1 1 1 | 0 0 1 1 1
------------+-----+------------+---------------+----------
x. x. ..    | 4 0 | 2 2  0 0 0 | 4 * * * * * * | 1 1 0 0 0
.. x.4o.    | 4 0 | 0 4  0 0 0 | * 2 * * * * * | 1 0 0 1 0
xx .. ..&#x | 2 2 | 1 0  2 1 0 | * * 8 * * * * | 0 1 1 0 0
.. xo ..&#x | 2 1 | 0 1  2 0 0 | * * * 8 * * * | 0 1 0 1 0
.. .. ox&#x | 1 2 | 0 0  2 0 1 | * * * * 8 * * | 0 0 1 1 0
.x .. .x    | 0 4 | 0 0  0 2 2 | * * * * * 4 * | 0 0 1 0 1
.. .o4.x    | 0 4 | 0 0  0 0 4 | * * * * * * 2 | 0 0 0 1 1
------------+-----+------------+---------------+----------
x. x.4o.     8 0 | 4 8  0 0 0 | 4 2 0 0 0 0 0 | 1 * * * *
xx xo ..&#x  4 2 | 2 2  4 1 0 | 1 0 2 2 0 0 0 | * 4 * * *
xx .. ox&#x  2 4 | 1 0  4 2 2 | 0 0 2 0 2 1 0 | * * 4 * *
.. xo4ox&#x  4 4 | 0 4  8 0 4 | 0 1 0 4 4 0 1 | * * * 2 *
.x .o4.x     0 8 | 0 0  0 4 8 | 0 0 0 0 0 4 2 | * * * * 1

s2s4s || s2s4s   → height = 1
(squap || squap)

demi( . . . )                 | 8 * | 1 1 2 1 0 0 0 | 1 3 1 1 2 0 0 | 1 1 3 0
                demi( . . . ) | * 8 | 0 0 0 1 1 1 2 | 0 0 1 1 2 1 3 | 0 1 3 1
------------------------------+-----+---------------+---------------+--------
      s2s .                   | 2 0 | 4 * * * * * * | 0 2 1 0 0 0 0 | 1 0 1 0
      s 2 s                   | 2 0 | * 4 * * * * * | 0 2 0 1 0 0 0 | 1 0 1 0
sefa( . s4s )                 | 2 0 | * * 8 * * * * | 1 1 0 0 1 0 0 | 1 1 1 0
demi( . . . ) || demi( . . . ) | 1 1 | * * * 8 * * * | 0 0 1 1 2 0 0 | 0 1 3 0
                      s2s .   | 0 2 | * * * * 4 * * | 0 0 1 0 0 0 2 | 0 0 2 1
                      s 2 s   | 0 2 | * * * * * 4 * | 0 0 0 1 0 0 2 | 0 0 2 1
                sefa( . s4s ) | 0 2 | * * * * * * 8 | 0 0 0 0 1 1 1 | 0 1 1 1
------------------------------+-----+---------------+---------------+--------
      . s4s                    4 0 | 0 0 4 0 0 0 0 | 2 * * * * * * | 1 1 0 0
sefa( s2s4s )                 | 3 0 | 1 1 1 0 0 0 0 | * 8 * * * * * | 1 0 1 0
      s2s .   ||       s2s .   | 2 2 | 1 0 0 2 1 0 0 | * * 4 * * * * | 0 0 2 0
      s 2 s   ||       s 2 s   | 2 2 | 0 1 0 2 0 1 0 | * * * 4 * * * | 0 0 2 0
sefa( . s4s ) || sefa( . s4s ) | 2 2 | 0 0 1 2 0 0 1 | * * * * 8 * * | 0 1 1 0
                      . s4s    0 4 | 0 0 0 0 0 0 4 | * * * * * 2 * | 0 1 0 1
                sefa( s2s4s ) | 0 3 | 0 0 0 0 1 1 1 | * * * * * * 8 | 0 0 1 1
------------------------------+-----+---------------+---------------+--------
      s2s4s                    8 0 | 4 4 8 0 0 0 0 | 2 8 0 0 0 0 0 | 1 * * *
      . s4s   ||       . s4s    4 4 | 0 0 4 4 0 0 4 | 1 0 0 0 4 1 0 | * 2 * *
sefa( s2s4s ) || sefa( s2s4s )  3 3 | 1 1 1 3 1 1 1 | 0 1 1 1 1 0 1 | * * 8 *
                      s2s4s    0 8 | 0 0 0 0 4 4 8 | 0 0 0 0 0 2 8 | * * * 1

s2s8o || s2s8o   → height = 1
(squap || squap)

demi( . . . )                 | 8 * | 2 2 1 0 0 | 1 3 2 2 0 0 | 1 1 3 0
                demi( . . . ) | * 8 | 0 0 1 2 2 | 0 0 2 2 1 3 | 0 1 3 1
------------------------------+-----+-----------+-------------+--------
      s2s .                   | 2 0 | 8 * * * * | 0 2 1 0 0 0 | 1 0 2 0
sefa( . s8o )                 | 2 0 | * 8 * * * | 1 1 0 1 0 0 | 1 1 1 0
demi( . . . ) || demi( . . . ) | 1 1 | * * 8 * * | 0 0 2 2 0 0 | 0 1 3 0
                      s2s . ) | 0 2 | * * * 8 * | 0 0 1 0 0 2 | 0 0 2 1
                sefa( . s8o ) | 0 2 | * * * * 8 | 0 0 0 1 1 1 | 0 1 1 1
------------------------------+-----+-----------+-------------+--------
      . s8o                    4 0 | 0 4 0 0 0 | 2 * * * * * | 1 1 0 0
sefa( s2s8o )                 | 3 0 | 2 1 0 0 0 | * 8 * * * * | 1 0 1 0
      s2s . ) ||       s2s . ) | 2 2 | 1 0 2 1 0 | * * 8 * * * | 0 0 2 0
sefa( . s8o ) || sefa( . s8o ) | 2 2 | 0 1 2 0 1 | * * * 8 * * | 0 1 1 0
                      . s8o    0 4 | 0 0 0 0 4 | * * * * 2 * | 0 1 0 1
                sefa( s2s8o ) | 0 3 | 0 0 0 2 1 | * * * * * 8 | 0 0 1 1
------------------------------+-----+-----------+-------------+--------
      s2s8o                    8 0 | 8 8 0 0 0 | 2 8 0 0 0 0 | 1 * * *
      . s8o   ||       . s8o    4 4 | 0 4 4 0 4 | 1 0 0 4 1 0 | * 2 * *
sefa( s2s8o ) || sefa( s2s8o )  3 3 | 2 1 3 2 1 | 0 1 2 1 0 1 | * * 8 *
                      s2s8o    0 8 | 0 0 0 8 8 | 0 0 0 0 2 8 | * * * 1

© 2004-2019
top of page