o x x     x o x
               
               
               
               
               
               
     x x x     

This polyteron is obtained from rappip if the latter is being seen as tepe || ope. Then ope gets reduced to its equatorial cube and the same faceting hyperplanes just marginally rasp at the pair of extremal squares of tepe.

Incidence matrix according to Dynkin symbol

oxx xox xxx&#x   → height(1,2) = 1/sqrt(2) = 0.707107
                   height(1,3) = height(2,3) = sqrt(3)/2 = 0.866025

o.. o.. o..    | 4 * * | 1 1 2 2 0 0 0 0 0 0 | 1 1 2 2 1 2 2 2 0 0 0 0 0 0 0 | 1 1 2 1 1 2 1 2 2 0 0 0 0 | 1 1 1 1 2 0
.o. .o. .o.    | * 4 * | 0 0 2 0 1 1 2 0 0 0 | 0 2 1 2 0 0 0 2 1 2 1 2 0 0 0 | 1 2 1 0 0 0 2 1 2 1 2 1 0 | 1 0 1 2 1 1
..o ..o ..o    | * * 8 | 0 0 0 1 0 0 1 1 1 1 | 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 | 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 1 1 1 1 1
---------------+-------+---------------------+-------------------------------+---------------------------+------------
... x.. ...    | 2 0 0 | 2 * * * * * * * * * | 1 0 2 0 0 2 0 0 0 0 0 0 0 0 0 | 1 0 2 1 0 2 0 2 0 0 0 0 0 | 1 1 1 0 2 0
... ... x..    | 2 0 0 | * 2 * * * * * * * * | 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 | 0 1 2 0 1 2 0 0 2 0 0 0 0 | 1 1 0 1 2 0
oo. oo. oo.&#x | 1 1 0 | * * 8 * * * * * * * | 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 1 1 1 0 0 0 0 | 1 0 1 1 1 0
o.o o.o o.o&#x | 1 0 1 | * * * 8 * * * * * * | 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    | 0 2 0 | * * * * 2 * * * * * | 0 2 0 0 0 0 0 0 1 2 0 0 0 0 0 | 1 2 0 0 0 0 2 0 0 1 2 0 0 | 1 0 1 2 0 1
... ... .x.    | 0 2 0 | * * * * * 2 * * * * | 0 0 0 2 0 0 0 0 1 0 0 2 0 0 0 | 0 2 1 0 0 0 0 0 2 0 2 1 0 | 1 0 0 2 1 1
.oo .oo .oo&#x | 0 1 1 | * * * * * * 8 * * * | 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 | 0 0 0 0 0 0 1 1 1 1 1 1 0 | 0 0 1 1 1 1
..x ... ...    | 0 0 2 | * * * * * * * 4 * * | 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 0 1 0 0 1 1 0 1 | 0 1 1 1 0 1
... ..x ...    | 0 0 2 | * * * * * * * * 4 * | 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 | 0 0 0 1 0 1 0 1 0 1 0 1 1 | 0 1 1 0 1 1
... ... ..x    | 0 0 2 | * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 | 0 0 0 0 1 1 0 0 1 0 1 1 1 | 0 1 0 1 1 1
---------------+-------+---------------------+-------------------------------+---------------------------+------------
... x.. x..    | 4 0 0 | 2 2 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 0 0 0 | 1 1 0 0 2 0
ox. ... ...&#x | 1 2 0 | 0 0 2 0 1 0 0 0 0 0 | * 4 * * * * * * * * * * * * * | 1 1 0 0 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
... xo. ...&#x | 2 1 0 | 1 0 2 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * | 1 0 1 0 0 0 0 1 0 0 0 0 0 | 1 0 1 0 1 0
... ... xx.&#x | 2 2 0 | 0 1 2 0 0 1 0 0 0 0 | * * * 4 * * * * * * * * * * * | 0 1 1 0 0 0 0 0 1 0 0 0 0 | 1 0 0 1 1 0
o.x ... ...&#x | 1 0 2 | 0 0 0 2 0 0 0 1 0 0 | * * * * 4 * * * * * * * * * * | 0 0 0 1 1 0 1 0 0 0 0 0 0 | 0 1 1 1 0 0
... x.x ...&#x | 2 0 2 | 1 0 0 2 0 0 0 0 1 0 | * * * * * 4 * * * * * * * * * | 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 1 1 0 1 0
... ... x.x&#x | 2 0 2 | 0 1 0 2 0 0 0 0 0 1 | * * * * * * 4 * * * * * * * * | 0 0 0 0 1 1 0 0 1 0 0 0 0 | 0 1 0 1 1 0
ooo ooo ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 0 | * * * * * * * 8 * * * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 1 1 1 0
.x. ... .x.    | 0 4 0 | 0 0 0 0 2 2 0 0 0 0 | * * * * * * * * 1 * * * * * * | 0 2 0 0 0 0 0 0 0 0 2 0 0 | 1 0 0 2 0 1
.xx ... ...&#x | 0 2 2 | 0 0 0 0 1 0 2 1 0 0 | * * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 1 0 0 1 1 0 0 | 0 0 1 1 0 1
... .ox ...&#x | 0 1 2 | 0 0 0 0 0 0 2 0 1 0 | * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 1 0 1 0 1 0 | 0 0 1 0 1 1
... ... .xx&#x | 0 2 2 | 0 0 0 0 0 1 2 0 0 1 | * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 1 1 1
..x ..x ...    | 0 0 4 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * 2 * * | 0 0 0 1 0 0 0 0 0 1 0 0 1 | 0 1 1 0 0 1
..x ... ..x    | 0 0 4 | 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * * * * 2 * | 0 0 0 0 1 0 0 0 0 0 1 0 1 | 0 1 0 1 0 1
... ..x ..x    | 0 0 4 | 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * 2 | 0 0 0 0 0 1 0 0 0 0 0 1 1 | 0 1 0 0 1 1
---------------+-------+---------------------+-------------------------------+---------------------------+------------
ox. xo. ...&#x ♦ 2 2 0 | 1 0 4 0 1 0 0 0 0 0 | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 1 0 1 0 0 0
ox. ... xx.&#x ♦ 2 4 0 | 0 1 4 0 2 2 0 0 0 0 | 0 2 0 2 0 0 0 0 1 0 0 0 0 0 0 | * 2 * * * * * * * * * * * | 1 0 0 1 0 0
... xo. xx.&#x ♦ 4 2 0 | 2 2 4 0 0 1 0 0 0 0 | 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * | 1 0 0 0 1 0
o.x x.x ...&#x ♦ 2 0 4 | 1 0 0 4 0 0 0 2 2 0 | 0 0 0 0 2 2 0 0 0 0 0 0 1 0 0 | * * * 2 * * * * * * * * * | 0 1 1 0 0 0
o.x ... x.x&#x ♦ 2 0 4 | 0 1 0 4 0 0 0 2 0 2 | 0 0 0 0 2 0 2 0 0 0 0 0 0 1 0 | * * * * 2 * * * * * * * * | 0 1 0 1 0 0
... x.x x.x&#x ♦ 4 0 4 | 2 2 0 4 0 0 0 0 2 2 | 1 0 0 0 0 2 2 0 0 0 0 0 0 0 1 | * * * * * 2 * * * * * * * | 0 1 0 0 1 0
oxx ... ...&#x ♦ 1 2 2 | 0 0 2 2 1 0 2 1 0 0 | 0 1 0 0 1 0 0 2 0 1 0 0 0 0 0 | * * * * * * 4 * * * * * * | 0 0 1 1 0 0
... xox ...&#x ♦ 2 1 2 | 1 0 2 2 0 0 2 0 1 0 | 0 0 1 0 0 1 0 2 0 0 1 0 0 0 0 | * * * * * * * 4 * * * * * | 0 0 1 0 1 0
... ... xxx&#x ♦ 2 2 2 | 0 1 2 2 0 1 2 0 0 1 | 0 0 0 1 0 0 1 2 0 0 0 1 0 0 0 | * * * * * * * * 4 * * * * | 0 0 0 1 1 0
.xx .ox ...&#x ♦ 0 2 4 | 0 0 0 0 1 0 4 2 2 0 | 0 0 0 0 0 0 0 0 0 2 2 0 1 0 0 | * * * * * * * * * 2 * * * | 0 0 1 0 0 1
.xx ... .xx&#x ♦ 0 4 4 | 0 0 0 0 2 2 4 2 0 2 | 0 0 0 0 0 0 0 0 1 2 0 2 0 1 0 | * * * * * * * * * * 2 * * | 0 0 0 1 0 1
... .ox .xx&#x ♦ 0 2 4 | 0 0 0 0 0 1 4 0 2 2 | 0 0 0 0 0 0 0 0 0 0 2 2 0 0 1 | * * * * * * * * * * * 2 * | 0 0 0 0 1 1
..x ..x ..x    ♦ 0 0 8 | 0 0 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * * * * 1 | 0 1 0 0 0 1
---------------+-------+---------------------+-------------------------------+---------------------------+------------
ox. xo. xx.&#x ♦ 4 4 0 | 2 2 8 0 2 2 0 0 0 0 | 1 4 4 4 0 0 0 0 1 0 0 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 0 | 1 * * * * *
o.x x.x x.x&#x ♦ 4 0 8 | 2 2 0 8 0 0 0 4 4 4 | 1 0 0 0 4 4 4 0 0 0 0 0 2 2 2 | 0 0 0 2 2 2 0 0 0 0 0 0 1 | * 1 * * * *
oxx xox ...&#x ♦ 2 2 4 | 1 0 4 4 1 0 4 2 2 0 | 0 2 2 0 2 2 0 4 0 2 2 0 1 0 0 | 1 0 0 1 0 0 2 2 0 1 0 0 0 | * * 2 * * *
oxx ... xxx&#x ♦ 2 4 4 | 0 1 4 4 2 2 4 2 0 2 | 0 2 0 2 2 0 2 4 1 2 0 2 0 1 0 | 0 1 0 0 1 0 2 0 2 0 1 0 0 | * * * 2 * *
... xox xxx&#x ♦ 4 2 4 | 2 2 4 4 0 1 4 0 2 2 | 1 0 2 2 0 2 2 4 0 0 2 2 0 0 1 | 0 0 1 0 0 1 0 2 2 0 0 1 0 | * * * * 2 *
.xx .ox .xx&#x ♦ 0 4 8 | 0 0 0 0 2 2 8 4 4 4 | 0 0 0 0 0 0 0 0 1 4 4 4 2 2 2 | 0 0 0 0 0 0 0 0 0 2 2 2 1 | * * * * * 1

tepe || cube   → height = sqrt(5/8) = 0.790569

  8 * | 1 2 1  2 0 0 | 3 1 2 2 1 2 2 0 0 | 1 3 3 2 1 1 2 0 | 1 1 1 3
  * 8 | 0 0 0  2 2 1 | 0 0 0 1 2 2 2 1 2 | 0 0 2 1 2 2 2 1 | 0 2 1 2
  ----+--------------+-------------------+-----------------+--------
  2 0 | 4 * *  * * * | 2 1 0 0 0 2 0 0 0 | 1 2 2 0 1 0 2 0 | 1 1 1 2 prism base para
  2 0 | * 8 *  * * * | 2 0 1 1 0 0 0 0 0 | 1 2 2 1 0 0 0 0 | 1 0 1 2 prism base other
  2 0 | * * 4  * * * | 0 1 2 0 0 0 2 0 0 | 0 3 0 2 0 1 2 0 | 1 1 0 3 prism lacing
  1 1 | * * * 16 * * | 0 0 0 1 1 1 1 0 0 | 0 0 2 1 1 1 1 0 | 0 1 1 2
  0 2 | * * *  * 8 * | 0 0 0 0 1 1 0 1 1 | 0 0 1 0 2 1 1 1 | 0 2 1 1 prism base
  0 2 | * * *  * * 4 | 0 0 0 0 0 0 2 0 2 | 0 0 0 1 0 2 2 1 | 0 2 0 2 prism lacing
  ----+--------------+-------------------+-----------------+--------
  3 0 | 1 2 0  0 0 0 | 8 * * * * * * * * | 1 1 1 0 0 0 0 0 | 1 0 1 1
  4 0 | 2 0 2  0 0 0 | * 2 * * * * * * * | 0 2 0 0 0 0 2 0 | 1 1 0 2
  4 0 | 0 2 2  0 0 0 | * * 4 * * * * * * | 0 2 0 1 0 0 0 0 | 1 0 0 2
  2 1 | 0 1 0  2 0 0 | * * * 8 * * * * * | 0 0 2 1 0 0 0 0 | 0 0 1 2
  1 2 | 0 0 0  2 1 0 | * * * * 8 * * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1
  2 2 | 1 0 0  2 1 0 | * * * * * 8 * * * | 0 0 1 0 1 0 1 0 | 0 1 1 1
  2 2 | 0 0 1  2 0 1 | * * * * * * 8 * * | 0 0 0 1 0 1 1 0 | 0 1 0 2
  0 4 | 0 0 0  0 4 0 | * * * * * * * 2 * | 0 0 0 0 2 0 0 1 | 0 2 1 0
  0 4 | 0 0 0  0 2 2 | * * * * * * * * 4 | 0 0 0 0 0 1 1 1 | 0 2 0 1
  ----+--------------+-------------------+-----------------+--------
♦ 4 0 | 2 4 0  0 0 0 | 4 0 0 0 0 0 0 0 0 | 2 * * * * * * * | 1 0 1 0
♦ 6 0 | 2 4 3  0 0 0 | 2 1 2 0 0 0 0 0 0 | * 4 * * * * * * | 1 0 0 1
♦ 3 2 | 1 2 0  4 1 0 | 1 0 0 2 1 1 0 0 0 | * * 8 * * * * * | 0 0 1 1
♦ 4 2 | 0 2 2  4 0 1 | 0 0 1 2 0 0 2 0 0 | * * * 4 * * * * | 0 0 0 2
♦ 2 4 | 1 0 0  4 4 0 | 0 0 0 0 2 2 0 1 0 | * * * * 4 * * * | 0 1 1 0
♦ 2 4 | 0 0 1  4 2 2 | 0 0 0 0 2 0 2 0 1 | * * * * * 4 * * | 0 1 0 1
♦ 4 4 | 2 0 2  4 2 2 | 0 1 0 0 0 2 2 0 1 | * * * * * * 4 * | 0 1 0 1
♦ 0 8 | 0 0 0  0 8 4 | 0 0 0 0 0 0 0 2 4 | * * * * * * * 1 | 0 2 0 0
  ----+--------------+-------------------+-----------------+--------
♦ 8 0 | 4 8 4  0 0 0 | 8 2 4 0 0 0 0 0 0 | 2 4 0 0 0 0 0 0 | 1 * * *
♦ 4 8 | 2 0 2  8 8 4 | 0 1 0 0 4 4 4 2 4 | 0 0 0 0 2 2 2 1 | * 2 * *
♦ 4 4 | 2 4 0  8 4 0 | 4 0 0 4 4 4 0 1 0 | 1 0 4 0 2 0 0 0 | * * 2 *
♦ 6 4 | 2 4 3  8 2 2 | 2 1 2 4 2 2 4 0 1 | 0 1 2 2 0 1 1 0 | * * * 4