Acronym esquidpyp
Name elongated square dipyramid prism,
J15 prism
Circumradius ...
Lace city
in approx. ASCII-art
      o x      o x      
                        
                        
o x   q x      q x   o x
                        
                        
      o x      o x      

 |     |        |     +-- line
 |     |        +-------- cube
 |     +----------------- cube
 +----------------------- line
      x x      
               
               
x x   w x   x x
               
               
      x x      
Coordinates
  • (1/2; 1/2, 1/2, 1/2)            & all changes of sign
  • (1/2; 0, 0, (1+sqrt(2))/2)   & all changes of sign
Face vector 20, 50, 44, 14
Confer
uniform relative:
ope   tes  
general polytopal classes:
CRF   partial Stott expansions  

This CRF can be obtained from ope by partial Stott expanding only within a single axial direction orthogonally to an equatorial cube cross-section. In fact it just inserts there a tes.


Incidence matrix according to Dynkin symbol

wx xx ox4oo&#zx

o. o. o.4o.     | 4  * | 4  4 0 0  0 | 4  4 0 0 0 | 1 4 0
.o .o .o4.o     | * 16 | 0  1 1 1  2 | 1  2 1 2 2 | 1 2 2
----------------+------+-------------+------------+------
.. x. .. ..     | 2  0 | 2  * * *  * | 4  0 0 0 0 | 0 4 0
oo oo oo4oo&#x  | 1  1 | * 16 * *  * | 1  2 0 0 0 | 1 2 0
.x .. .. ..     | 0  2 | *  * 8 *  * | 0  0 1 2 0 | 1 0 2
.. .x .. ..     | 0  2 | *  * * 8  * | 1  0 1 0 2 | 0 2 2
.. .. .x ..     | 0  2 | *  * * * 16 | 0  1 0 1 1 | 1 1 1
----------------+------+-------------+------------+------
.. xx .. ..&#x  | 2  2 | 1  2 0 1  0 | 8  * * * * | 0 2 0
.. .. ox ..&#x  | 1  2 | 0  2 0 0  1 | * 16 * * * | 1 1 0
.x .x .. ..     | 0  4 | 0  0 2 2  0 | *  * 4 * * | 0 0 2
.x .. .x ..     | 0  4 | 0  0 2 0  2 | *  * * 8 * | 1 0 1
.. .x .x ..     | 0  4 | 0  0 0 2  2 | *  * * * 8 | 0 1 1
----------------+------+-------------+------------+------
wx .. ox4oo&#zx  2  8 | 0  8 4 0  8 | 0  8 0 4 0 | 2 * *
.. xx ox ..&#x   2  4 | 1  4 0 2  2 | 2  2 0 0 1 | * 8 *
.x .x .x ..      0  8 | 0  0 4 4  4 | 0  0 2 2 2 | * * 4

(wx)(wx) (ox)(ox)4(oo)(oo)&#(zx)

(o.)(..) (o.)(..)4(o.)(..)       | 2 * * * | 4 1 0 0 0 0 0 0 | 4 4 0 0 0 0 0 | 1 4 0 0
(.o)(..) (.o)(..)4(.o)(..)       | * 8 * * | 1 0 1 2 1 0 0 0 | 2 1 2 1 2 0 0 | 1 2 2 0
(..)(o.) (..)(o.)4(..)(o.)       | * * 2 * | 0 1 0 0 0 4 0 0 | 0 4 0 0 0 4 0 | 0 4 0 1
(..)(.o) (..)(.o)4(..)(.o)       | * * * 8 | 0 0 0 0 1 1 1 2 | 0 1 0 1 2 2 2 | 0 2 2 1
---------------------------------+---------+-----------------+---------------+--------
(oo)(..) (oo)(..)4(oo)(..)&#x    | 1 1 0 0 | 8 * * * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0
(o.)(o.) (o.)(o.)4(o.)(o.)&#x    | 1 0 1 0 | * 2 * * * * * * | 0 4 0 0 0 0 0 | 0 4 0 0
(.x)(..) (..)(..)4(..)(..)       | 0 2 0 0 | * * 4 * * * * * | 0 0 2 1 0 0 0 | 1 0 2 0
(..)(..) (.x)(..)4(..)(..)       | 0 2 0 0 | * * * 8 * * * * | 1 0 1 0 1 0 0 | 1 1 1 0
(.o)(.o) (.o)(.o)4(.o)(.o)&#x    | 0 1 0 1 | * * * * 8 * * * | 0 1 0 1 2 0 0 | 0 2 2 0
(..)(oo) (..)(oo)4(..)(oo)&#x    | 0 0 1 1 | * * * * * 8 * * | 0 1 0 0 0 2 0 | 0 2 0 1
(..)(.x) (..)(..)4(..)(..)       | 0 0 0 2 | * * * * * * 4 * | 0 0 0 1 0 0 2 | 0 0 2 1
(..)(..) (..)(.x)4(..)(..)       | 0 0 0 2 | * * * * * * * 8 | 0 0 0 0 1 1 1 | 0 1 1 1
---------------------------------+---------+-----------------+---------------+--------
(..)(..) (ox)(..)4(..)(..)&#x    | 1 2 0 0 | 2 0 0 1 0 0 0 0 | 8 * * * * * * | 1 1 0 0
(oo)(oo) (oo)(oo)4(oo)(oo)&#xr   | 1 1 1 1 | 1 1 0 0 1 1 0 0 | * 8 * * * * * | 0 2 0 0	cycle (ABDC)
(.x)(..) (.x)(..)4(..)(..)       | 0 4 0 0 | 0 0 2 2 0 0 0 0 | * * 4 * * * * | 1 0 1 0
(.x)(.x) (..)(..)4(..)(..)&#x    | 0 2 0 2 | 0 0 1 0 2 0 1 0 | * * * 4 * * * | 0 0 2 0
(..)(..) (.x)(.x)4(..)(..)&#x    | 0 2 0 2 | 0 0 0 1 2 0 0 1 | * * * * 8 * * | 0 1 1 0
(..)(..) (..)(ox)4(..)(..)&#x    | 0 0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * 8 * | 0 1 0 1
(..)(.x) (..)(.x)4(..)(..)       | 0 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * 4 | 0 0 1 1
---------------------------------+---------+-----------------+---------------+--------
(wx)(..) (ox)(..)4(oo)(..)&#(zx)  2 8 0 0 | 8 0 4 8 0 0 0 0 | 8 0 4 0 0 0 0 | 1 * * *
(..)(..) (ox)(ox)4(..)(..)&#xr    1 2 1 2 | 2 1 0 1 2 2 0 1 | 1 2 0 0 1 1 0 | * 8 * *	cycle (ABDC)
(.x)(.x) (.x)(.x)4(..)(..)&#x     0 4 0 4 | 0 0 2 2 4 0 2 2 | 0 0 1 2 2 0 1 | * * 4 *
(..)(wx) (..)(ox)4(..)(oo)&#(zx)  0 0 2 8 | 0 0 0 0 0 8 4 8 | 0 0 0 0 0 8 4 | * * * 1

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