Acronym pextet
Name partially (edge-)expanded tetrahedron
 
Vertex figure [3,3,r,r], [3,R,R]
Dihedral angles
(at margins)
  • between {(r,R)2} and {3}:   arccos(-1/sqrt(3)) = 125.264390°
  • between {(r,R)2} and {(r,R)2}:   90°
  • between {3} and {3}:   arccos(1/3) = 70.528779°
Confer
uniform relative:
tet  
related CnRFs:
pabextet   patex cube  
general polytopal classes:
partial Stott expansions  

The vertex angles of the rhombs {(r,R)2} are r = 45° resp. R = 135°.

Note that the x distances provided in the tower description in its tropal layers are pseudo edges only.


Incidence matrix according to Dynkin symbol

xoxo oxox&#xt   → outer heights = 1/sqrt(2) = 0.707107
                  inner height = 1-1/sqrt(2) = 0.292893

o... o...     | 2 * * * | 1 2 1 0 0 0 | 2 2 0  [3,3,r,r]
.o.. .o..     | * 2 * * | 0 2 0 1 0 0 | 1 2 0  [3,R,R]
..o. ..o.     | * * 2 * | 0 0 1 0 2 0 | 0 2 1  [3,R,R]
...o ...o     | * * * 2 | 0 0 0 1 2 1 | 0 2 2  [3,3,r,r]
--------------+---------+-------------+------
x... ....     | 2 0 0 0 | 1 * * * * * | 2 0 0
oo.. oo..&#x  | 1 1 0 0 | * 4 * * * * | 1 1 0
o.o. o.o.&#x  | 1 0 1 0 | * * 2 * * * | 0 2 0
.o.o .o.o&#x  | 0 1 0 1 | * * * 2 * * | 0 2 0
..oo ..oo&#x  | 0 0 1 1 | * * * * 4 * | 0 1 1
.... ...x     | 0 0 0 2 | * * * * * 1 | 0 0 2
--------------+---------+-------------+------
xo.. ....&#x  | 2 1 0 0 | 1 2 0 0 0 0 | 2 * *
oooo oooo&#xr | 1 1 1 1 | 0 1 1 1 1 0 | * 4 *  {(r,R)2} - ring: (ABDC)
.... ..ox&#x  | 0 0 1 2 | 0 0 0 0 2 1 | * * 2
or
o... o...     & | 4 * | 1 2 1 | 2 2  [3,3,r,r]
.o.. .o..     & | * 4 | 0 2 1 | 1 2  [3,R,R]
----------------+-----+-------+----
x... ....     & | 2 0 | 2 * * | 2 0
oo.. oo..&#x  & | 1 1 | * 8 * | 1 1
o.o. o.o.&#x  & | 1 1 | * * 4 | 0 2
----------------+-----+-------+----
xo.. ....&#x  & | 2 1 | 1 2 0 | 4 *
oooo oooo&#xr   | 2 2 | 0 2 2 | * 4  {(r,R)2} - ring: (ABDC)

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