Acronym pent
Name penteract,
decateron,
5D measure-polytope5),
geopet(id)
|,>,O device line prism prism prism prism = |||||
Field of sections
 ©
Circumradius sqrt(5)/2 = 1.118034
Inradius 1/2
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o3o4o o3o3o3o . . o3o3o4o
1o3o3o3o4x o3o3o3o .
vertex first
. o3o3o4x
tes first
2 o3o3o3q .
vertex figure
. o3o3o4x
opposite tes
3 o3o3q3o .  
4 o3q3o3o .
5 q3o3o3o .
6 o3o3o3o .
opposite vertex
Lace city
in approx. ASCII-art
c c     with c = x4o3o  or  x x4o  or  x x x  (cube)
c c
Coordinates (1/2, 1/2, 1/2, 1/2, 1/2)   & all changes of sign
Dual tac
Dihedral angles
Confer
general multiprisms:
n,cube-dip   n,m-dippip  
general polytopal classes:
hypercube   partial Stott expansions   segmentotera  
External
links
hedrondude   wikipedia   mathworld

Its equatorial cross-section in vertex first orientation is not a vertex layer. Even so it can be determined as 1/q-deca (cf. truncation series).


Incidence matrix according to Dynkin symbol

o3o3o3o4x

. . . . . | 32   5 | 10 | 10 |  5
----------+----+----+----+----+---
. . . . x |  2 | 80   4 |  6 |  4
----------+----+----+----+----+---
. . . o4x |  4 |  4 | 80 |  3 |  3
----------+----+----+----+----+---
. . o3o4x   8 | 12 |  6 | 40 |  2
----------+----+----+----+----+---
. o3o3o4x  16 | 32 | 24 |  8 | 10

snubbed forms: o3o3o3o4s

o3o3o3o4/3x

. . . .   . | 32   5 | 10 | 10 |  5
------------+----+----+----+----+---
. . . .   x |  2 | 80   4 |  6 |  4
------------+----+----+----+----+---
. . . o4/3x |  4 |  4 | 80 |  3 |  3
------------+----+----+----+----+---
. . o3o4/3x   8 | 12 |  6 | 40 |  2
------------+----+----+----+----+---
. o3o3o4/3x  16 | 32 | 24 |  8 | 10

o4x o3o4x

. . . . . | 32   2  3 | 1  6  3 |  3  6 1 | 3 2
----------+----+-------+---------+---------+----
. x . . . |  2 | 32  *  1  3  0 |  3  3 0 | 3 1
. . . . x |  2 |  * 48  0  2  2 |  1  4 1 | 2 2
----------+----+-------+---------+---------+----
o4x . . . |  4 |  4  0 | 8  *  * |  3  0 0 | 3 0
. x . . x |  4 |  2  2 | * 48  * |  1  2 0 | 2 1
. . . o4x |  4 |  0  4 | *  * 24 |  0  2 1 | 1 2
----------+----+-------+---------+---------+----
o4x . . x   8 |  8  4 | 2  4  0 | 12  * * | 2 0
. x . o4x   8 |  4  8 | 0  4  2 |  * 24 * | 1 1
. . o3o4x   8 |  0 12 | 0  0  6 |  *  * 4 | 0 2
----------+----+-------+---------+---------+----
o4x . o4x  16 | 16 16 | 4 16  4 |  4  4 0 | 6 *
. x o3o4x  16 |  8 24 | 0 12 12 |  0  6 2 | * 4

x o3o3o4x

. . . . . | 32   1  4 |  4  6 |  6  4 | 4 1
----------+----+-------+-------+-------+----
x . . . . |  2 | 16  *   4  0 |  6  0 | 4 0
. . . . x |  2 |  * 64   1  3 |  3  3 | 3 1
----------+----+-------+-------+-------+----
x . . . x |  4 |  2  2 | 32  * |  3  0 | 3 0
. . . o4x |  4 |  0  4 |  * 48 |  1  2 | 2 1
----------+----+-------+-------+-------+----
x . . o4x   8 |  4  8 |  4  2 | 24  * | 2 0
. . o3o4x   8 |  0 12 |  0  6 |  * 16 | 1 1
----------+----+-------+-------+-------+----
x . o3o4x  16 |  8 24 | 12 12 |  6  2 | 8 *
. o3o3o4x  16 |  0 32 |  0 24 |  0  8 | * 2

x o4x o4x

. . . . . | 32   1  2  2 |  2  2 1  4 1 | 1  4 1 2 2 | 2 2 1
----------+----+----------+--------------+------------+------
x . . . . |  2 | 16  *  *   2  2 0  0 0 | 1  4 1 0 0 | 2 2 0
. . x . . |  2 |  * 32  *   1  0 1  2 0 | 1  2 0 2 1 | 2 1 1
. . . . x |  2 |  *  * 32   0  1 0  2 1 | 0  2 1 1 2 | 1 2 1
----------+----+----------+--------------+------------+------
x . x . . |  4 |  2  2  0 | 16  * *  * * | 1  2 0 0 0 | 2 1 0
x . . . x |  4 |  2  0  2 |  * 16 *  * * | 0  2 1 0 0 | 1 2 0
. o4x . . |  4 |  0  4  0 |  *  * 8  * * | 1  0 0 2 0 | 2 0 1
. . x . x |  4 |  0  2  2 |  *  * * 32 * | 0  1 0 1 1 | 1 1 1
. . . o4x |  4 |  0  0  4 |  *  * *  * 8 | 0  0 1 0 2 | 0 2 1
----------+----+----------+--------------+------------+------
x o4x . .   8 |  4  8  0 |  4  0 2  0 0 | 4  * * * * | 2 0 0
x . x . x   8 |  4  4  4 |  2  2 0  2 0 | * 16 * * * | 1 1 0
x . . o4x   8 |  4  0  8 |  0  4 0  0 2 | *  * 4 * * | 0 2 0
. o4x . x   8 |  0  8  4 |  0  0 2  4 0 | *  * * 8 * | 1 0 1
. . x o4x   8 |  0  4  8 |  0  0 0  4 2 | *  * * * 8 | 0 1 1
----------+----+----------+--------------+------------+------
x o4x . x  16 |  8 16  8 |  8  4 4  8 0 | 2  4 0 2 0 | 4 * *
x . x o4x  16 |  8  8 16 |  4  8 0  8 4 | 0  4 2 0 2 | * 4 *
. o4x o4x  16 |  0 16 16 |  0  0 4 16 4 | 0  0 0 4 4 | * * 2

x x o3o4x

. . . . . | 32   1  1  3 | 1  3  3  3 |  3  3  3 1 | 3 1 1
----------+----+----------+------------+------------+------
x . . . . |  2 | 16  *  *  1  3  0  0 |  3  3  0 0 | 3 1 0
. x . . . |  2 |  * 16  *  1  0  3  0 |  3  0  3 0 | 3 0 1
. . . . x |  2 |  *  * 48  0  1  1  2 |  1  2  2 1 | 2 1 1
----------+----+----------+------------+------------+------
x x . . . |  4 |  2  2  0 | 8  *  *  * |  3  0  0 0 | 3 0 0
x . . . x |  4 |  2  0  2 | * 24  *  * |  1  2  0 0 | 2 1 0
. x . . x |  4 |  0  2  2 | *  * 24  * |  1  0  2 0 | 2 0 1
. . . o4x |  4 |  0  0  4 | *  *  * 24 |  0  1  1 1 | 1 1 1
----------+----+----------+------------+------------+------
x x . . x   8 |  4  4  4 | 2  2  2  0 | 12  *  * * | 2 0 0
x . . o4x   8 |  4  0  8 | 0  4  0  2 |  * 12  * * | 1 1 0
. x . o4x   8 |  0  4  8 | 0  0  4  2 |  *  * 12 * | 1 0 1
. . o3o4x   8 |  0  0 12 | 0  0  0  6 |  *  *  * 4 | 0 1 1
----------+----+----------+------------+------------+------
x x . o4x  16 |  8  8 16 | 4  8  8  4 |  4  2  2 0 | 6 * *
x . o3o4x  16 |  8  0 24 | 0 12  0 12 |  0  6  0 2 | * 2 *
. x o3o4x  16 |  0  8 24 | 0  0 12 12 |  0  0  6 2 | * * 2

x x x o4x

. . . . . | 32   1  1  1  2 | 1 1  2 1  2  2 1 | 1 2 2 1 2 1 1 | 2 1 1 1
----------+----+-------------+------------------+---------------+--------
x . . . . |  2 | 16  *  *  *  1 1  2 0  0  0 0 | 1 2 2 1 0 0 0 | 2 1 1 0
. x . . . |  2 |  * 16  *  *  1 0  0 1  2  0 0 | 1 2 0 0 2 1 0 | 2 1 0 1
. . x . . |  2 |  *  * 16  *  0 1  0 1  0  2 0 | 1 0 2 0 2 0 1 | 2 0 1 1
. . . . x |  2 |  *  *  * 32  0 0  1 0  1  1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
----------+----+-------------+------------------+---------------+--------
x x . . . |  4 |  2  2  0  0 | 8 *  * *  *  * * | 1 2 0 0 0 0 0 | 2 1 0 0
x . x . . |  4 |  2  0  2  0 | * 8  * *  *  * * | 1 0 2 0 0 0 0 | 2 0 1 0
x . . . x |  4 |  2  0  0  2 | * * 16 *  *  * * | 0 1 1 1 0 0 0 | 1 1 1 0
. x x . . |  4 |  0  2  2  0 | * *  * 8  *  * * | 1 0 0 0 2 0 0 | 2 0 0 1
. x . . x |  4 |  0  2  0  2 | * *  * * 16  * * | 0 1 0 0 1 1 0 | 1 1 0 1
. . x . x |  4 |  0  0  2  2 | * *  * *  * 16 * | 0 0 1 0 1 0 1 | 1 0 1 1
. . . o4x |  4 |  0  0  0  4 | * *  * *  *  * 8 | 0 0 0 1 0 1 1 | 0 1 1 1
----------+----+-------------+------------------+---------------+--------
x x x . .   8 |  4  4  4  0 | 2 2  0 2  0  0 0 | 4 * * * * * * | 2 0 0 0
x x . . x   8 |  4  4  0  4 | 2 0  2 0  2  0 0 | * 8 * * * * * | 1 1 0 0
x . x . x   8 |  4  0  4  4 | 0 2  2 0  0  2 0 | * * 8 * * * * | 1 0 1 0
x . . o4x   8 |  4  0  0  8 | 0 0  4 0  0  0 2 | * * * 4 * * * | 0 1 1 0
. x x . x   8 |  0  4  4  4 | 0 0  0 2  2  2 0 | * * * * 8 * * | 1 0 0 1
. x . o4x   8 |  0  4  0  8 | 0 0  0 0  4  0 2 | * * * * * 4 * | 0 1 0 1
. . x o4x   8 |  0  0  4  8 | 0 0  0 0  0  4 2 | * * * * * * 4 | 0 0 1 1
----------+----+-------------+------------------+---------------+--------
x x x . x  16 |  8  8  8  8 | 4 4  4 4  4  4 0 | 2 2 2 0 2 0 0 | 4 * * *
x x . o4x  16 |  8  8  0 16 | 4 0  8 0  8  0 4 | 0 4 0 2 0 2 0 | * 2 * *
x . x o4x  16 |  8  0  8 16 | 0 4  8 0  0  8 4 | 0 0 4 2 0 0 2 | * * 2 *
. x x o4x  16 |  0  8  8 16 | 0 0  0 4  8  8 4 | 0 0 0 0 4 2 2 | * * * 2

x x x x x

. . . . . | 32   1  1  1  1  1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
----------+----+----------------+---------------------+---------------------+----------
x . . . . |  2 | 16  *  *  *  *  1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
. x . . . |  2 |  * 16  *  *  *  1 0 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
. . x . . |  2 |  *  * 16  *  *  0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
. . . x . |  2 |  *  *  * 16  *  0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1
. . . . x |  2 |  *  *  *  * 16  0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
----------+----+----------------+---------------------+---------------------+----------
x x . . . |  4 |  2  2  0  0  0 | 8 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
x . x . . |  4 |  2  0  2  0  0 | * 8 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
x . . x . |  4 |  2  0  0  2  0 | * * 8 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
x . . . x |  4 |  2  0  0  0  2 | * * * 8 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
. x x . . |  4 |  0  2  2  0  0 | * * * * 8 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
. x . x . |  4 |  0  2  0  2  0 | * * * * * 8 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
. x . . x |  4 |  0  2  0  0  2 | * * * * * * 8 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
. . x x . |  4 |  0  0  2  2  0 | * * * * * * * 8 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
. . x . x |  4 |  0  0  2  0  2 | * * * * * * * * 8 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
. . . x x |  4 |  0  0  0  2  2 | * * * * * * * * * 8 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
----------+----+----------------+---------------------+---------------------+----------
x x x . .   8 |  4  4  4  0  0 | 2 2 0 0 2 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0
x x . x .   8 |  4  4  0  4  0 | 2 0 2 0 0 2 0 0 0 0 | * 4 * * * * * * * * | 1 0 1 0 0
x x . . x   8 |  4  4  0  0  4 | 2 0 0 2 0 0 2 0 0 0 | * * 4 * * * * * * * | 0 1 1 0 0
x . x x .   8 |  4  0  4  4  0 | 0 2 2 0 0 0 0 2 0 0 | * * * 4 * * * * * * | 1 0 0 1 0
x . x . x   8 |  4  0  4  0  4 | 0 2 0 2 0 0 0 0 2 0 | * * * * 4 * * * * * | 0 1 0 1 0
x . . x x   8 |  4  0  0  4  4 | 0 0 2 2 0 0 0 0 0 2 | * * * * * 4 * * * * | 0 0 1 1 0
. x x x .   8 |  0  4  4  4  0 | 0 0 0 0 2 2 0 2 0 0 | * * * * * * 4 * * * | 1 0 0 0 1
. x x . x   8 |  0  4  4  0  4 | 0 0 0 0 2 0 2 0 2 0 | * * * * * * * 4 * * | 0 1 0 0 1
. x . x x   8 |  0  4  0  4  4 | 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * 4 * | 0 0 1 0 1
. . x x x   8 |  0  0  4  4  4 | 0 0 0 0 0 0 0 2 2 2 | * * * * * * * * * 4 | 0 0 0 1 1
----------+----+----------------+---------------------+---------------------+----------
x x x x .  16 |  8  8  8  8  0 | 4 4 4 0 4 4 0 4 0 0 | 2 2 0 2 0 0 2 0 0 0 | 2 * * * *
x x x . x  16 |  8  8  8  0  8 | 4 4 0 4 4 0 4 0 4 0 | 2 0 2 0 2 0 0 2 0 0 | * 2 * * *
x x . x x  16 |  8  8  0  8  8 | 4 0 4 4 0 4 4 0 0 4 | 0 2 2 0 0 2 0 0 2 0 | * * 2 * *
x . x x x  16 |  8  0  8  8  8 | 0 4 4 4 0 0 0 4 4 4 | 0 0 0 2 2 2 0 0 0 2 | * * * 2 *
. x x x x  16 |  0  8  8  8  8 | 0 0 0 0 4 4 4 4 4 4 | 0 0 0 0 0 0 2 2 2 2 | * * * * 2

oo3oo3oo4xx&#x   → height = 1
(tes || tes)

o.3o.3o.4o.    | 16  *   4  1  0 |  6  4  0 | 4  6 0 | 1 4 0
.o3.o3.o4.o    |  * 16   0  1  4 |  0  4  6 | 0  6 4 | 0 4 1
---------------+-------+----------+----------+--------+------
.. .. .. x.    |  2  0 | 32  *  *   3  1  0 | 3  3 0 | 1 3 0
oo3oo3oo4oo&#x |  1  1 |  * 16  *   0  4  0 | 0  6 0 | 0 4 0
.. .. .. .x    |  0  2 |  *  * 32   0  1  3 | 0  3 3 | 0 3 1
---------------+-------+----------+----------+--------+------
.. .. o.4x.    |  4  0 |  4  0  0 | 24  *  * | 2  1 0 | 1 2 0
.. .. .. xx&#x |  2  2 |  1  2  1 |  * 32  * | 0  3 0 | 0 3 0
.. .. .o4.x    |  0  4 |  0  0  4 |  *  * 24 | 0  1 2 | 0 2 1
---------------+-------+----------+----------+--------+------
.. o.3o.4x.      8  0 | 12  0  0 |  6  0  0 | 8  * * | 1 1 0
.. .. oo4xx&#x   4  4 |  4  4  4 |  1  4  1 | * 24 * | 0 2 0
.. .o3.o4.x      0  8 |  0  0 12 |  0  0  6 | *  * 8 | 0 1 1
---------------+-------+----------+----------+--------+------
o.3o.3o.4x.     16  0 | 32  0  0 | 24  0  0 | 8  0 0 | 1 * *
.. oo3oo4xx&#x   8  8 | 12  8 12 |  6 12  6 | 1  6 1 | * 8 *
.o3.o3.o4.x      0 16 |  0  0 32 |  0  0 24 | 0  0 8 | * * 1

oqo ooo3ooo4xxx&#xt   → both heights = 1/sqrt(2) = 0.707107
(cube || pseudo (x,x,x,q)-tes || cube)

o.. o..3o..4o..     | 8  * *   3  2  0  0  0 | 3  6 1  0  0 0 | 1  6  3 0  0 0 | 2 3 0
.o. .o.3.o.4.o.     | * 16 *   0  1  3  1  0 | 0  3 1  3  3 0 | 0  3  3 1  3 0 | 1 3 1
..o ..o3..o4..o     | *  * 8   0  0  0  2  3 | 0  0 1  0  6 3 | 0  0  3 0  6 1 | 0 3 2
--------------------+--------+----------------+----------------+----------------+------
... ... ... x..     | 2  0 0 | 12  *  *  *  *  2  2 0  0  0 0 | 1  4  1 0  0 0 | 2 2 0
oo. oo.3oo.4oo.&#x  | 1  1 0 |  * 16  *  *  *  0  3 1  0  0 0 | 0  3  3 0  0 0 | 1 3 0
... ... ... .x.     | 0  2 0 |  *  * 24  *  *  0  1 0  2  1 0 | 0  2  1 1  2 0 | 1 2 1
.oo .oo3.oo4.oo&#x  | 0  1 1 |  *  *  * 16  *  0  0 1  0  3 0 | 0  0  3 0  3 0 | 0 3 1
... ... ... ..x     | 0  0 2 |  *  *  *  * 12  0  0 0  0  2 2 | 0  0  1 0  4 1 | 0 2 2
--------------------+--------+----------------+----------------+----------------+------
... ... o..4x..     | 4  0 0 |  4  0  0  0  0 | 6  * *  *  * * | 1  2  0 0  0 0 | 2 1 0
... ... ... xx.&#x  | 2  2 0 |  1  2  1  0  0 | * 24 *  *  * * | 0  2  1 0  0 0 | 1 2 0
oqo ... ... ...&#xt | 1  2 1 |  0  2  0  2  0 | *  * 8  *  * * | 0  0  3 0  0 0 | 0 3 0
... ... .o.4.x.     | 0  4 0 |  0  0  4  0  0 | *  * * 12  * * | 0  1  0 1  1 0 | 1 1 1
... ... ... .xx&#x  | 0  2 2 |  0  0  1  2  1 | *  * *  * 24 * | 0  0  1 0  2 0 | 0 2 1
... ... ..o4..x     | 0  0 4 |  0  0  0  0  4 | *  * *  *  * 6 | 0  0  0 0  2 1 | 0 1 2
--------------------+--------+----------------+----------------+----------------+------
... o..3o..4x..      8  0 0 | 12  0  0  0  0 | 6  0 0  0  0 0 | 1  *  * *  * * | 2 0 0
... ... oo.4xx.&#x   4  4 0 |  4  4  4  0  0 | 1  4 0  1  0 0 | * 12  * *  * * | 1 1 0
oqo ... ... xxx&#xt  2  4 2 |  1  4  2  4  1 | 0  2 2  0  2 0 | *  * 12 *  * * | 0 2 0
... .o.3.o.4.x.      0  8 0 |  0  0 12  0  0 | 0  0 0  6  0 0 | *  *  * 2  * * | 1 0 1
... ... .oo4.xx&#x   0  4 4 |  0  0  4  4  4 | 0  0 0  1  4 1 | *  *  * * 12 * | 0 1 1
... ..o3..o4..x      0  0 8 |  0  0  0  0 12 | 0  0 0  0  0 6 | *  *  * *  * 1 | 0 0 2
--------------------+--------+----------------+----------------+----------------+------
... oo.3oo.4xx.&#x   8  8 0 | 12  8 12  0  0 | 6 12 0  6  0 0 | 1  6  0 1  0 0 | 2 * *
oqo ... ooo4xxx&#xt  4  8 4 |  4  8  8  8  4 | 1  8 4  2  8 1 | 0  2  4 0  2 0 | * 6 *
... .oo3.oo4.xx&#x   0  8 8 |  0  0 12  8 12 | 0  0 0  6 12 6 | 0  0  0 1  6 1 | * * 2
or
o.. o..3o..4o..      & | 16  *   3  2  0 |  3  6 1  0 | 1  6  3 0 | 2 3
.o. .o.3.o.4.o.        |  * 16   0  2  3 |  0  6 1  3 | 0  6  3 1 | 2 3
-----------------------+-------+----------+------------+-----------+----
... ... ... x..      & |  2  0 | 24  *  *   2  2 0  0 | 1  4  1 0 | 2 2
oo. oo.3oo.4oo.&#x   & |  1  1 |  * 32  *   0  3 1  0 | 0  3  3 0 | 1 3
... ... ... .x.        |  0  2 |  *  * 24   0  2 0  2 | 0  4  1 1 | 2 2
-----------------------+-------+----------+------------+-----------+----
... ... o..4x..      & |  4  0 |  4  0  0 | 12  * *  * | 1  2  0 0 | 2 1
... ... ... xx.&#x   & |  2  2 |  1  2  1 |  * 48 *  * | 0  2  1 0 | 1 2
oqo ... ... ...&#xt    |  2  2 |  0  4  0 |  *  * 8  * | 0  0  3 0 | 0 3
... ... .o.4.x.        |  0  4 |  0  0  4 |  *  * * 12 | 0  2  0 1 | 2 1
-----------------------+-------+----------+------------+-----------+----
... o..3o..4x..      &   8  0 | 12  0  0 |  6  0 0  0 | 2  *  * * | 2 0
... ... oo.4xx.&#x   &   4  4 |  4  4  4 |  1  4 0  1 | * 24  * * | 1 1
oqo ... ... xxx&#xt      4  4 |  2  8  2 |  0  4 2  0 | *  * 12 * | 0 2
... .o.3.o.4.x.          0  8 |  0  0 12 |  0  0 0  6 | *  *  * 2 | 2 0
-----------------------+-------+----------+------------+-----------+----
... oo.3oo.4xx.&#x   &   8  8 | 12  8 12 |  6 12 0  6 | 1  6  0 1 | 4 *
oqo ... ooo4xxx&#xt      8  8 |  8 16  8 |  2 16 4  2 | 0  4  4 0 | * 6

oqoo3ooqo xxxx4oooo&#xt   → all heights = 1/sqrt(3) = 0.577350
({4} || pseudo (q,x)-tisdip || pseudo (dual q, para x)-tisdip || {4})

o...3o... o...4o...      & | 8  *  2  3  0  0 | 1  6  3 0  0 | 3  6 1 0 | 3 2
.o..3.o.. .o..4.o..      & | * 24  0  1  2  2 | 0  2  3 1  4 | 1  6 1 2 | 3 2
---------------------------+------+------------+--------------+----------+----
.... .... x... ....      & | 2  0 | 8  *  *  *  1  3  0 0  0 | 3  3 0 0 | 3 1
oo..3oo.. oo..4oo..&#x   & | 1  1 | * 24  *  *  0  2  2 0  0 | 1  4 1 0 | 2 2
.... .... .x.. ....      & | 0  2 | *  * 24  *  0  1  0 1  2 | 1  3 0 2 | 3 1
.oo.3.oo. .oo.4.oo.&#x     | 0  2 | *  *  * 24  0  0  2 0  2 | 0  4 1 1 | 2 2
---------------------------+------+------------+--------------+----------+----
.... .... x...4o...      & | 4  0 | 4  0  0  0 | 2  *  * *  * | 3  0 0 0 | 3 0
.... .... xx.. ....&#x   & | 2  2 | 1  2  1  0 | * 24  * *  * | 1  2 0 0 | 2 1
oqo. .... .... ....&#xt  & | 1  3 | 0  2  0  2 | *  * 24 *  * | 0  2 1 0 | 1 2
.... .... .x..4.o..      & | 0  4 | 0  0  4  0 | *  *  * 6  * | 1  0 0 2 | 3 0
.... .... .xx. ....&#x     | 0  4 | 0  0  2  2 | *  *  * * 24 | 0  2 0 1 | 2 1
---------------------------+------+------------+--------------+----------+----
.... .... xx..4oo..&#x   &  4  4 | 4  4  4  0 | 1  4  0 1  0 | 6  * * * | 2 0
oqo. .... xxx. ....&#xt  &  2  6 | 1  4  3  4 | 0  2  2 0  2 | * 24 * * | 1 1
oqoo3ooqo .... ....&#xt     2  6 | 0  6  0  6 | 0  0  6 0  0 | *  * 4 * | 0 2
.... .... .xx.4.oo.&#x      0  8 | 0  0  8  4 | 0  0  0 2  4 | *  * * 6 | 2 0
---------------------------+------+------------+--------------+----------+----
oqo. .... xxx.4ooo.&#xt  &  4 12 | 4  8 12  8 | 1  8  4 3  8 | 2  4 0 2 | 6 *
oqoo3ooqo xxxx ....&#xt     4 12 | 2 12  6 12 | 0  6 12 0  6 | 0  6 2 0 | * 4

xxxxx oqooo3ooqoo3oooqo&#xt   → all heights = 1/2
(line || pseudo (q,x)-tepe || pseudo (q,x)-ope || pseudo inv (q,x)-tepe || line)

o.... o....3o....3o....      & | 4  *  *  1  4 0  0 0 | 4  6  0  0 |  6  4  0 | 4 1
.o... .o...3.o...3.o...      & | * 16  *  0  1 1  3 0 | 1  3  3  3 |  3  4  3 | 4 1
..o.. ..o..3..o..3..o..      & | *  * 12  0  0 0  4 1 | 0  2  4  4 |  2  4  4 | 4 1
-------------------------------+---------+-------------+------------+----------+----
x.... ..... ..... .....      & | 2  0  0 | 2  * *  * *  4  0  0  0 |  6  0  0 | 4 0
oo... oo...3oo...3oo...&#x   & | 1  1  0 | * 16 *  * *  1  3  0  0 |  3  3  0 | 3 1
.x... ..... ..... .....      & | 0  2  0 | *  * 8  * *  1  0  3  0 |  3  0  3 | 4 0
.oo.. .oo..3.oo..3.oo..&#x   & | 0  1  1 | *  * * 48 *  0  1  1  2 |  1  3  2 | 3 1
..x.. ..... ..... .....        | 0  0  2 | *  * *  * 6  0  0  4  0 |  2  0  4 | 4 0
-------------------------------+---------+-------------+------------+----------+----
xx... ..... ..... .....&#x   & | 2  2  0 | 1  2 1  0 0 | 8  *  *  * |  3  0  0 | 3 0
..... oqo.. ..... .....&#xt  & | 1  2  1 | 0  2 0  2 0 | * 24  *  * |  1  2  0 | 2 1
.xx.. ..... ..... .....&#x   & | 0  2  2 | 0  0 1  2 1 | *  * 24  * |  1  0  2 | 3 0
..... ..... .oqo. .....&#xt    | 0  2  2 | 0  0 0  4 0 | *  *  * 24 |  0  2  1 | 2 1
-------------------------------+---------+-------------+------------+----------+----
xxx.. oqo.. ..... .....&#xt  &  2  4  2 | 1  4 2  4 1 | 2  2  2  0 | 12  *  * | 2 0
..... oqoo.3ooqo. .....&#xt  &  1  4  3 | 0  3 0  9 0 | 0  3  0  3 |  * 16  * | 1 1
.xxx. ..... .oqo. .....&#xt     0  4  4 | 0  0 2  8 2 | 0  0  4  2 |  *  * 12 | 2 0
-------------------------------+---------+-------------+------------+----------+----
xxxx. oqoo.3ooqo. .....&#xt  &  2  8  6 | 1  6 4 18 3 | 3  6  9  6 |  3  2  3 | 8 *
..... oqooo3ooqoo3oooqo&#xt     2  8  6 | 0  8 0 24 0 | 0 12  0 12 |  0  8  0 | * 2

oqoooo3ooqooo3oooqoo3ooooqo&#xt   → all heights = 1/sqrt(5) = 0.447214
(pt || pseudo q-pen || pseudo q-rap || pseudo inv q-rap || pseudo dual q-pen || pt)

o.....3o.....3o.....3o.....     | 1 *  *  * * *  5  0  0  0 0 | 10  0  0  0 | 10  0  0 | 5 0
.o....3.o....3.o....3.o....     | * 5  *  * * *  1  4  0  0 0 |  4  6  0  0 |  6  4  0 | 4 1
..o...3..o...3..o...3..o...     | * * 10  * * *  0  2  3  0 0 |  1  6  3  0 |  3  6  1 | 3 2
...o..3...o..3...o..3...o..     | * *  * 10 * *  0  0  3  2 0 |  0  3  6  1 |  1  6  3 | 2 3
....o.3....o.3....o.3....o.     | * *  *  * 5 *  0  0  0  4 1 |  0  0  6  4 |  0  4  6 | 1 4
.....o3.....o3.....o3.....o     | * *  *  * * 1  0  0  0  0 5 |  0  0  0 10 |  0  0 10 | 0 5
--------------------------------+---------------+--------------+-------------+----------+----
oo....3oo....3oo....3oo....&#x  | 1 1  0  0 0 0 | 5  *  *  * *   4  0  0  0 |  6  0  0 | 4 0
.oo...3.oo...3.oo...3.oo...&#x  | 0 1  1  0 0 0 | * 20  *  * *   1  3  0  0 |  3  3  0 | 3 1
..oo..3..oo..3..oo..3..oo..&#x  | 0 0  1  1 0 0 | *  * 30  * *   0  2  2  0 |  1  4  1 | 2 2
...oo.3...oo.3...oo.3...oo.&#x  | 0 0  0  1 1 0 | *  *  * 20 *   0  0  3  1 |  0  3  3 | 1 3
....oo3....oo3....oo3....oo&#x  | 0 0  0  0 1 1 | *  *  *  * 5   0  0  0  4 |  0  0  6 | 0 4
--------------------------------+---------------+--------------+-------------+----------+----
oqo... ...... ...... ......&#xt | 1 2  1  0 0 0 | 2  2  0  0 0 | 10  *  *  * |  3  0  0 | 3 0
...... .oqo.. ...... ......&#xt | 0 1  2  1 0 0 | 0  2  2  0 0 |  * 30  *  * |  1  2  0 | 2 1
...... ...... ..oqo. ......&#xt | 0 0  1  2 1 0 | 0  0  2  2 0 |  *  * 30  * |  0  2  1 | 1 2
...... ...... ...... ...oqo&#xt | 0 0  0  1 2 1 | 0  0  0  2 2 |  *  *  * 10 |  0  0  3 | 0 3
--------------------------------+---------------+--------------+-------------+----------+----
oqoo..3ooqo.. ...... ......&#xt  1 3  3  1 0 0 | 3  6  3  0 0 |  3  3  0  0 | 10  *  * | 2 0
...... .oqoo.3.ooqo. ......&#xt  0 1  3  3 1 0 | 0  3  6  3 0 |  0  3  3  0 |  * 20  * | 1 1
...... ...... ..oqoo3..ooqo&#xt  0 0  1  3 3 1 | 0  0  3  6 3 |  0  0  3  3 |  *  * 10 | 0 2
--------------------------------+---------------+--------------+-------------+----------+----
oqooo.3ooqoo.3oooqo. ......&#xt  1 4  6  4 1 0 | 4 12 12  4 0 |  6 12  6  0 |  4  4  0 | 5 *
...... .oqooo3.ooqoo3.oooqo&#xt  0 1  4  6 4 1 | 0  4 12 12 4 |  0  6 12  6 |  0  4  4 | * 5
or
o.....3o.....3o.....3o.....      & | 2  *  *   5  0  0 | 10  0 | 10  0 |  5
.o....3.o....3.o....3.o....      & | * 10  *   1  4  0 |  4  6 |  6  4 |  5
..o...3..o...3..o...3..o...      & | *  * 20   0  2  3 |  1  9 |  4  6 |  5
-----------------------------------+---------+----------+-------+-------+---
oo....3oo....3oo....3oo....&#x   & | 1  1  0 | 10  *  *   4  0 |  6  0 |  4
.oo...3.oo...3.oo...3.oo...&#x   & | 0  1  1 |  * 40  *   1  3 |  3  3 |  4
..oo..3..oo..3..oo..3..oo..&#x     | 0  0  2 |  *  * 30   0  4 |  2  4 |  4
-----------------------------------+---------+----------+-------+-------+---
oqo... ...... ...... ......&#xt  & | 1  2  1 |  2  2  0 | 20  * |  3  0 |  3
...... .oqo.. ...... ......&#xt  & | 0  1  3 |  0  2  2 |  * 60 |  1  2 |  3
-----------------------------------+---------+----------+-------+-------+---
oqoo..3ooqo.. ...... ......&#xt  &  1  3  4 |  3  6  3 |  3  3 | 20  * |  2
...... .oqoo.3.ooqo. ......&#xt     0  2  6 |  0  6  6 |  0  6 |  * 20 |  2
-----------------------------------+---------+----------+-------+-------+---
oqooo.3ooqoo.3oooqo. ......&#xt  &  1  5 10 |  4 16 12 |  6 18 |  4  4 | 10

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