Name small cellated dodecateron,
small hedrated dodecateron,
stericated hexateron,
expanded hexateron,
vertex figure of cyxh,
lattice A5 contact polytope (span of its roots)
Field of sections
` ©`
wrt. pen
sqrt(3/5) = 0.774597
wrt. tepe
sqrt(3/8) = 0.612372
wrt. triddip
1/sqrt(3) = 0.577350
Vertex figure
` ©    ©`
Lace city
in approx. ASCII-art
```  o     t    		-- o3o3o3x (pen)

T     C     t		-- x3o3o3x (spid)

T     o  		-- x3o3o3o (dual pen)

\     \     +--	x  x3o3o (tepe)
\     +-------	uo ox3oo3ox
+------------	x  o3o3x (inv. tepe)

where:
o - o3o3o (point)
t - x3o3o (tet)
C - x3o3x (co)
T - o3o3x (dual tet)
```
 ``` © ``` ``` o o + - o - # + o + - o o where: o = equatorial vertices +,- = mutually dual triangles above/below # = equatorial hexagon ```
Lace hyper city
in approx. ASCII-art
 ``` t t t x3o x3o (triddip) ``` ``` o o o H o o o compound of x3x o3o and o3o x3x ``` ``` T T T o3x o3x (bidual triddip) ```
```where:
o = o3o
t = x3o
T = o3x
H = x3x
```
Volume 21 sqrt(3)/40 = 0.909327
Surface (30+20 sqrt(2)+sqrt(5))/8 = 7.565042
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
 by cells: duhd pen piphid spid tepe triddip dehad 6 12 0 0 0 0 dacox 0 12 6 0 15 0 dibhid 0 12 0 6 0 20 scad 0 12 0 0 30 20 bacox 0 0 6 0 15 20 chad 0 0 0 6 30 0
& others)
Dihedral angles
(at margins)
Confer
related segmentotera:
penaspid   penatrip   pexhix   tepaco
general polytopal classes:
lace simplices
analogs:
maximal epanded simplex eSn
External

Incidence matrix according to Dynkin symbol

```x3o3o3o3x

. . . . . | 30 ♦  4  4 |  6 12  6 |  4 12 12  4 | 1  4  6  4 1
----------+----+-------+----------+-------------+-------------
x . . . . |  2 | 60  * |  3  3  0 |  3  6  3  0 | 1  3  3  1 0
. . . . x |  2 |  * 60 |  0  3  3 |  0  3  6  3 | 0  1  3  3 1
----------+----+-------+----------+-------------+-------------
x3o . . . |  3 |  3  0 | 60  *  * |  2  2  0  0 | 1  2  1  0 0
x . . . x |  4 |  2  2 |  * 90  * |  0  2  2  0 | 0  1  2  1 0
. . . o3x |  3 |  0  3 |  *  * 60 |  0  0  2  2 | 0  0  1  2 1
----------+----+-------+----------+-------------+-------------
x3o3o . . ♦  4 |  6  0 |  4  0  0 | 30  *  *  * | 1  1  0  0 0
x3o . . x ♦  6 |  6  3 |  2  3  0 |  * 60  *  * | 0  1  1  0 0
x . . o3x ♦  6 |  3  6 |  0  3  2 |  *  * 60  * | 0  0  1  1 0
. . o3o3x ♦  4 |  0  6 |  0  0  4 |  *  *  * 30 | 0  0  0  1 1
----------+----+-------+----------+-------------+-------------
x3o3o3o . ♦  5 | 10  0 | 10  0  0 |  5  0  0  0 | 6  *  *  * *
x3o3o . x ♦  8 | 12  4 |  8  6  0 |  2  4  0  0 | * 15  *  * *
x3o . o3x ♦  9 |  9  9 |  3  9  3 |  0  3  3  0 | *  * 20  * *
x . o3o3x ♦  8 |  4 12 |  0  6  8 |  0  0  4  2 | *  *  * 15 *
. o3o3o3x ♦  5 |  0 10 |  0  0 10 |  0  0  0  5 | *  *  *  * 6
```
```or
. . . . .    | 30 ♦   8 |  12 12 |  8  24 |  2  8  6
-------------+----+-----+--------+--------+---------
x . . . .  & |  2 | 120 |   3  3 |  3   9 |  1  4  3
-------------+----+-----+--------+--------+---------
x3o . . .  & |  3 |   3 | 120  * |  2   2 |  1  2  1
x . . . x    |  4 |   4 |   * 90 |  0   4 |  0  2  2
-------------+----+-----+--------+--------+---------
x3o3o . .  & ♦  4 |   6 |   4  0 | 60   * |  1  1  0
x3o . . x  & ♦  6 |   9 |   2  3 |  * 120 |  0  1  1
-------------+----+-----+--------+--------+---------
x3o3o3o .  & ♦  5 |  10 |  10  0 |  5   0 | 12  *  *
x3o3o . x  & ♦  8 |  16 |   8  6 |  2   4 |  * 30  *
x3o . o3x    ♦  9 |  18 |   6  9 |  0   6 |  *  * 20
```

```xxo3ooo3ooo3oxx&#xt   → both heights = sqrt(3/5) = 0.774597
(pen || pseudo spid || dual pen)

o..3o..3o..3o..    | 5  * * ♦  4  4  0  0  0  0 |  6 12  6  0  0  0  0  0  0 | 4 12 12  4 0  0  0 0  0  0  0 0 | 1 4  6  4 1 0  0  0 0 0
.o.3.o.3.o.3.o.    | * 20 * ♦  0  1  3  3  1  0 |  0  3  3  3  6  3  3  3  0 | 0  3  6  3 1  3  3 1  3  6  3 0 | 0 1  3  3 1 1  3  3 1 0
..o3..o3..o3..o    | *  * 5 ♦  0  0  0  0  4  4 |  0  0  0  0  0  0  6 12  6 | 0  0  0  0 0  0  0 0  4 12 12 4 | 0 0  0  0 0 1  4  6 4 1
-------------------+--------+-------------------+----------------------------+---------------------------------+------------------------
x.. ... ... ...    | 2  0 0 | 10  *  *  *  *  * |  3  3  0  0  0  0  0  0  0 | 3  6  3  0 0  0  0 0  0  0  0 0 | 1 3  3  1 0 0  0  0 0 0
oo.3oo.3oo.3oo.&#x | 1  1 0 |  * 20  *  *  *  * |  0  3  3  0  0  0  0  0  0 | 0  3  6  3 0  0  0 0  0  0  0 0 | 0 1  3  3 1 0  0  0 0 0
.x. ... ... ...    | 0  2 0 |  *  * 30  *  *  * |  0  1  0  2  2  0  1  0  0 | 0  2  2  0 1  2  1 0  2  2  0 0 | 0 1  2  1 0 1  2  1 0 0
... ... ... .x.    | 0  2 0 |  *  *  * 30  *  * |  0  0  1  0  2  2  0  1  0 | 0  0  2  2 0  1  2 1  0  2  2 0 | 0 0  1  2 1 0  1  2 1 0
.oo3.oo3.oo3.oo&#x | 0  1 1 |  *  *  *  * 20  * |  0  0  0  0  0  0  3  3  0 | 0  0  0  0 0  0  0 0  3  6  3 0 | 0 0  0  0 0 1  3  3 1 0
... ... ... ..x    | 0  0 2 |  *  *  *  *  * 10 |  0  0  0  0  0  0  0  3  3 | 0  0  0  0 0  0  0 0  0  3  6 3 | 0 0  0  0 0 0  1  3 3 1
-------------------+--------+-------------------+----------------------------+---------------------------------+------------------------
x..3o.. ... ...    | 3  0 0 |  3  0  0  0  0  0 | 10  *  *  *  *  *  *  *  * | 2  2  0  0 0  0  0 0  0  0  0 0 | 1 2  1  0 0 0  0  0 0 0
xx. ... ... ...&#x | 2  2 0 |  1  2  1  0  0  0 |  * 30  *  *  *  *  *  *  * | 0  2  2  0 0  0  0 0  0  0  0 0 | 0 1  2  1 0 0  0  0 0 0
... ... ... ox.&#x | 1  2 0 |  0  2  0  1  0  0 |  *  * 30  *  *  *  *  *  * | 0  0  2  2 0  0  0 0  0  0  0 0 | 0 0  1  2 1 0  0  0 0 0
.x.3.o. ... ...    | 0  3 0 |  0  0  3  0  0  0 |  *  *  * 20  *  *  *  *  * | 0  1  0  0 1  1  0 0  1  0  0 0 | 0 1  1  0 0 1  1  0 0 0
.x. ... ... .x.    | 0  4 0 |  0  0  2  2  0  0 |  *  *  *  * 30  *  *  *  * | 0  0  1  0 0  1  1 0  0  1  0 0 | 0 0  1  1 0 0  1  1 0 0
... ... .o.3.x.    | 0  3 0 |  0  0  0  3  0  0 |  *  *  *  *  * 20  *  *  * | 0  0  0  1 0  0  1 1  0  0  1 0 | 0 0  0  1 1 0  0  1 1 0
.xo ... ... ...&#x | 0  2 1 |  0  0  1  0  2  0 |  *  *  *  *  *  * 30  *  * | 0  0  0  0 0  0  0 0  2  2  0 0 | 0 0  0  0 0 1  2  1 0 0
... ... ... .xx&#x | 0  2 2 |  0  0  0  1  2  1 |  *  *  *  *  *  *  * 30  * | 0  0  0  0 0  0  0 0  0  2  2 0 | 0 0  0  0 0 0  1  2 1 0
... ... ..o3..x    | 0  0 3 |  0  0  0  0  0  3 |  *  *  *  *  *  *  *  * 10 | 0  0  0  0 0  0  0 0  0  0  2 2 | 0 0  0  0 0 0  0  1 2 1
-------------------+--------+-------------------+----------------------------+---------------------------------+------------------------
x..3o..3o.. ...    ♦ 4  0 0 |  6  0  0  0  0  0 |  4  0  0  0  0  0  0  0  0 | 5  *  *  * *  *  * *  *  *  * * | 1 1  0  0 0 0  0  0 0 0
xx.3oo. ... ...&#x ♦ 3  3 0 |  3  3  3  0  0  0 |  1  3  0  1  0  0  0  0  0 | * 20  *  * *  *  * *  *  *  * * | 0 1  1  0 0 0  0  0 0 0
xx. ... ... ox.&#x ♦ 2  4 0 |  1  4  2  2  0  0 |  0  2  2  0  1  0  0  0  0 | *  * 30  * *  *  * *  *  *  * * | 0 0  1  1 0 0  0  0 0 0
... ... oo.3ox.&#x ♦ 1  3 0 |  0  3  0  3  0  0 |  0  0  3  0  0  1  0  0  0 | *  *  * 20 *  *  * *  *  *  * * | 0 0  0  1 1 0  0  0 0 0
.x.3.o.3.o. ...    ♦ 0  4 0 |  0  0  6  0  0  0 |  0  0  0  4  0  0  0  0  0 | *  *  *  * 5  *  * *  *  *  * * | 0 1  0  0 0 1  0  0 0 0
.x.3.o. ... .x.    ♦ 0  6 0 |  0  0  6  3  0  0 |  0  0  0  2  3  0  0  0  0 | *  *  *  * * 10  * *  *  *  * * | 0 0  1  0 0 0  1  0 0 0
.x. ... .o.3.x.    ♦ 0  6 0 |  0  0  3  6  0  0 |  0  0  0  0  3  2  0  0  0 | *  *  *  * *  * 10 *  *  *  * * | 0 0  0  1 0 0  0  1 0 0
... .o.3.o.3.x.    ♦ 0  4 0 |  0  0  0  6  0  0 |  0  0  0  0  0  4  0  0  0 | *  *  *  * *  *  * 5  *  *  * * | 0 0  0  0 1 0  0  0 1 0
.xo3.oo ... ...&#x ♦ 0  3 1 |  0  0  3  0  3  0 |  0  0  0  1  0  0  3  0  0 | *  *  *  * *  *  * * 20  *  * * | 0 0  0  0 0 1  1  0 0 0
.xo ... ... .xx&#x ♦ 0  4 2 |  0  0  2  2  4  1 |  0  0  0  0  1  0  2  2  0 | *  *  *  * *  *  * *  * 30  * * | 0 0  0  0 0 0  1  1 0 0
... ... .oo3.xx&#x ♦ 0  3 3 |  0  0  0  3  3  3 |  0  0  0  0  0  1  0  3  1 | *  *  *  * *  *  * *  *  * 20 * | 0 0  0  0 0 0  0  1 1 0
... ..o3..o3..x    ♦ 0  0 4 |  0  0  0  0  0  6 |  0  0  0  0  0  0  0  0  4 | *  *  *  * *  *  * *  *  *  * 5 | 0 0  0  0 0 0  0  0 1 1
-------------------+--------+-------------------+----------------------------+---------------------------------+------------------------
x..3o..3o..3o..    ♦ 5  0 0 | 10  0  0  0  0  0 | 10  0  0  0  0  0  0  0  0 | 5  0  0  0 0  0  0 0  0  0  0 0 | 1 *  *  * * *  *  * * *
xx.3oo.3oo. ...&#x ♦ 4  4 0 |  6  4  6  0  0  0 |  4  6  0  4  0  0  0  0  0 | 1  4  0  0 1  0  0 0  0  0  0 0 | * 5  *  * * *  *  * * *
xx.3oo. ... ox.&#x ♦ 3  6 0 |  3  6  6  3  0  0 |  1  6  3  2  3  0  0  0  0 | 0  2  3  0 0  1  0 0  0  0  0 0 | * * 10  * * *  *  * * *
xx. ... oo.3ox.&#x ♦ 2  6 0 |  1  6  3  6  0  0 |  0  3  6  0  3  2  0  0  0 | 0  0  3  2 0  0  1 0  0  0  0 0 | * *  * 10 * *  *  * * *
... oo.3oo.3ox.&#x ♦ 1  4 0 |  0  4  0  6  0  0 |  0  0  6  0  0  4  0  0  0 | 0  0  0  4 0  0  0 1  0  0  0 0 | * *  *  * 5 *  *  * * *
.xo3.oo3.oo ...&#x ♦ 0  4 1 |  0  0  6  0  4  0 |  0  0  0  4  0  0  6  0  0 | 0  0  0  0 1  0  0 0  4  0  0 0 | * *  *  * * 5  *  * * *
.xo3.oo ... .xx&#x ♦ 0  6 2 |  0  0  6  3  6  1 |  0  0  0  2  3  0  6  3  0 | 0  0  0  0 0  1  0 0  2  3  0 0 | * *  *  * * * 10  * * *
.xo ... .oo3.xx&#x ♦ 0  6 3 |  0  0  3  6  6  3 |  0  0  0  0  3  2  3  6  1 | 0  0  0  0 0  0  1 0  0  3  2 0 | * *  *  * * *  * 10 * *
... .oo3.oo3.xx&#x ♦ 0  4 4 |  0  0  0  6  4  6 |  0  0  0  0  0  4  0  6  4 | 0  0  0  0 0  0  0 1  0  0  4 1 | * *  *  * * *  *  * 5 *
..o3..o3..o3..x    ♦ 0  0 5 |  0  0  0  0  0 10 |  0  0  0  0  0  0  0  0 10 | 0  0  0  0 0  0  0 0  0  0  0 5 | * *  *  * * *  *  * * 1
```
```or
o..3o..3o..3o..    & | 10  * ♦  4  4  0 |  6 12  6  0  0 |  4 12 12  4  0  0 | 1  4  6  4  1
.o.3.o.3.o.3.o.      |  * 20 ♦  0  2  6 |  0  6  6  6  6 |  0  6 12  6  2  6 | 0  2  6  6  2
---------------------+-------+----------+----------------+-------------------+--------------
x.. ... ... ...    & |  2  0 | 20  *  * |  3  3  0  0  0 |  3  6  3  0  0  0 | 1  3  3  1  0
oo.3oo.3oo.3oo.&#x & |  1  1 |  * 40  * |  0  3  3  0  0 |  0  3  6  3  0  0 | 0  1  3  3  1
.x. ... ... ...    & |  0  2 |  *  * 60 |  0  1  1  2  2 |  0  2  4  2  1  3 | 0  1  3  3  1
---------------------+-------+----------+----------------+-------------------+--------------
x..3o.. ... ...    & |  3  0 |  3  0  0 | 20  *  *  *  * |  2  2  0  0  0  0 | 1  2  1  0  0
xx. ... ... ...&#x & |  2  2 |  1  2  1 |  * 60  *  *  * |  0  2  2  0  0  0 | 0  1  2  1  0
... ... ... ox.&#x & |  1  2 |  0  2  1 |  *  * 60  *  * |  0  0  2  2  0  0 | 0  0  1  2  1
.x.3.o. ... ...    & |  0  3 |  0  0  3 |  *  *  * 40  * |  0  1  0  1  1  1 | 0  1  1  1  1
.x. ... ... .x.      |  0  4 |  0  0  4 |  *  *  *  * 30 |  0  0  2  0  0  2 | 0  0  2  2  0
---------------------+-------+----------+----------------+-------------------+--------------
x..3o..3o.. ...    & ♦  4  0 |  6  0  0 |  4  0  0  0  0 | 10  *  *  *  *  * | 1  1  0  0  0
xx.3oo. ... ...&#x & ♦  3  3 |  3  3  3 |  1  3  0  1  0 |  * 40  *  *  *  * | 0  1  1  0  0
xx. ... ... ox.&#x & ♦  2  4 |  1  4  4 |  0  2  2  0  1 |  *  * 60  *  *  * | 0  0  1  1  0
... ... oo.3ox.&#x & ♦  1  3 |  0  3  3 |  0  0  3  1  0 |  *  *  * 40  *  * | 0  0  0  1  1
.x.3.o.3.o. ...    & ♦  0  4 |  0  0  6 |  0  0  0  4  0 |  *  *  *  * 10  * | 0  1  0  0  1
.x.3.o. ... .x.    & ♦  0  6 |  0  0  9 |  0  0  0  2  3 |  *  *  *  *  * 20 | 0  0  1  1  0
---------------------+-------+----------+----------------+-------------------+--------------
x..3o..3o..3o..    & ♦  5  0 | 10  0  0 | 10  0  0  0  0 |  5  0  0  0  0  0 | 2  *  *  *  *
xx.3oo.3oo. ...&#x & ♦  4  4 |  6  4  6 |  4  6  0  4  0 |  1  4  0  0  1  0 | * 10  *  *  *
xx.3oo. ... ox.&#x & ♦  3  6 |  3  6  9 |  1  6  3  2  3 |  0  2  3  0  0  1 | *  * 20  *  *
xx. ... oo.3ox.&#x & ♦  2  6 |  1  6  9 |  0  3  6  2  3 |  0  0  3  2  0  1 | *  *  * 20  *
... oo.3oo.3ox.&#x & ♦  1  4 |  0  4  6 |  0  0  6  4  0 |  0  0  0  4  1  0 | *  *  *  * 10
```

```x(xo)o3o(xo)x x(ox)o3o(ox)x&#xt   → all heights = 1/sqrt(3) = 0.577350
(triddip || pseudo ({6} x pt, pt x {6})-compound † || bi-inv triddip)

o(..).3o(..). o(..).3o(..).     & | 18  * ♦  2  2  2  2 0 0 | 1  4 1  2  1  4  4  2  1  4 | 2 2  4  2  2  2  4  2  6  6 | 1 2 1 2 1  5 2 2
.(o.).3.(o.). .(o.).3.(o.).     & |  * 12 ♦  0  0  3  3 1 1 | 0  0 0  3  3  3  3  3  3  6 | 0 0  3  3  1  1  3  3  9  9 | 0 1 1 1 1  6 3 3
----------------------------------+-------+-----------------+-----------------------------+-----------------------------+-----------------
x(..). .(..). .(..). .(..).     & |  2  0 | 18  *  *  * * * | 1  2 0  1  0  0  2  0  0  0 | 2 1  2  0  0  2  2  1  2  0 | 1 1 0 2 1  2 1 0
.(..). .(..). x(..). .(..).     & |  2  0 |  * 18  *  * * * | 0  2 1  0  0  2  0  1  0  0 | 1 2  2  1  2  0  2  0  0  2 | 1 2 1 1 0  2 0 1
o(o.).3o(o.). o(o.).3o(o.).&#x  & |  1  1 |  *  * 36  * * * | 0  0 0  1  1  2  0  0  0  2 | 0 0  2  2  1  0  0  0  3  4 | 0 1 1 0 0  3 1 2
o(.o).3o(.o). o(.o).3o(.o).&#x  & |  1  1 |  *  *  * 36 * * | 0  0 0  0  0  0  2  1  1  2 | 0 0  0  0  0  1  2  2  4  3 | 0 0 0 1 1  3 2 1
.(x.). .(..). .(..). .(..).     & |  0  2 |  *  *  *  * 6 * | 0  0 0  3  0  0  0  0  3  0 | 0 0  3  0  0  0  0  3  6  0 | 0 1 0 0 1  3 3 0
.(..). .(x.). .(..). .(..).     & |  0  2 |  *  *  *  * * 6 | 0  0 0  0  3  0  0  3  0  0 | 0 0  0  3  0  0  3  0  0  6 | 0 0 1 1 0  3 0 3
----------------------------------+-------+-----------------+-----------------------------+-----------------------------+-----------------
x(..).3o(..). .(..). .(..).     & |  3  0 |  3  0  0  0 0 0 | 6  * *  *  *  *  *  *  *  * | 2 0  0  0  0  2  0  0  0  0 | 1 0 0 2 1  0 0 0
x(..). .(..). x(..). .(..).     & |  4  0 |  2  2  0  0 0 0 | * 18 *  *  *  *  *  *  *  * | 1 1  1  0  0  0  1  0  0  0 | 1 1 0 1 0  1 0 0
.(..). .(..). x(..).3o(..).     & |  3  0 |  0  3  0  0 0 0 | *  * 6  *  *  *  *  *  *  * | 0 2  0  0  2  0  0  0  0  0 | 1 2 1 0 0  0 0 0
x(x.). .(..). .(..). .(..).&#x  & |  2  2 |  1  0  2  0 1 0 | *  * * 18  *  *  *  *  *  * | 0 0  2  0  0  0  0  0  2  0 | 0 1 0 0 0  2 1 0
.(..). o(x.). .(..). .(..).&#x  & |  1  2 |  0  0  2  0 0 1 | *  * *  * 18  *  *  *  *  * | 0 0  0  2  0  0  0  0  0  2 | 0 0 1 0 0  1 0 2
.(..). .(..). x(o.). .(..).&#x  & |  2  1 |  0  1  2  0 0 0 | *  * *  *  * 36  *  *  *  * | 0 0  1  1  1  0  0  0  0  1 | 0 1 1 0 0  1 0 1
x(.o). .(..). .(..). .(..).&#x  & |  2  1 |  1  0  0  2 0 0 | *  * *  *  *  * 36  *  *  * | 0 0  0  0  0  1  1  1  1  0 | 0 0 0 1 1  1 1 0
.(..). .(..). x(.x). .(..).&#x  & |  2  2 |  0  1  0  2 0 1 | *  * *  *  *  *  * 18  *  * | 0 0  0  0  0  0  2  0  0  2 | 0 0 0 1 0  2 0 1
.(..). .(..). .(..). o(.x).&#x  & |  1  2 |  0  0  0  2 1 0 | *  * *  *  *  *  *  * 18  * | 0 0  0  0  0  0  0  2  2  0 | 0 0 0 0 1  1 2 0
o(oo)o o(oo)o o(oo)o o(oo)o&#xr   |  2  2 |  0  0  2  2 0 0 | *  * *  *  *  *  *  *  * 36 | 0 0  0  0  0  0  0  0  2  2 | 0 0 0 0 0  2 1 1
----------------------------------+-------+-----------------+-----------------------------+-----------------------------+-----------------
x(..).3o(..). x(..). .(..).     & ♦  6  0 |  6  3  0  0 0 0 | 2  3 0  0  0  0  0  0  0  0 | 6 *  *  *  *  *  *  *  *  * | 1 0 0 1 0  0 0 0
x(..). .(..). x(..).3o(..).     & ♦  6  0 |  3  6  0  0 0 0 | 0  3 2  0  0  0  0  0  0  0 | * 6  *  *  *  *  *  *  *  * | 1 1 0 0 0  0 0 0
x(x.). .(..). x(o.). .(..).&#x  & ♦  4  2 |  2  2  4  0 1 0 | 0  1 0  2  0  2  0  0  0  0 | * * 18  *  *  *  *  *  *  * | 0 1 0 0 0  1 0 0
.(..). o(x.). x(o.). .(..).&#x  & ♦  2  2 |  0  1  4  0 0 1 | 0  0 0  0  2  2  0  0  0  0 | * *  * 18  *  *  *  *  *  * | 0 0 1 0 0  0 0 1
.(..). .(..). x(o.).3o(o.).&#x  & ♦  3  1 |  0  3  3  0 0 0 | 0  0 1  0  0  3  0  0  0  0 | * *  *  * 12  *  *  *  *  * | 0 1 1 0 0  0 0 0
x(.o).3o(.o). .(..). .(..).&#x  & ♦  3  1 |  3  0  0  3 0 0 | 1  0 0  0  0  0  3  0  0  0 | * *  *  *  * 12  *  *  *  * | 0 0 0 1 1  0 0 0
x(.o). .(..). x(.x). .(..).&#x  & ♦  4  2 |  2  2  0  4 0 1 | 0  1 0  0  0  0  2  2  0  0 | * *  *  *  *  * 18  *  *  * | 0 0 0 1 0  1 0 0
x(.o). .(..). .(..). o(.x).&#x  & ♦  2  2 |  1  0  0  4 1 0 | 0  0 0  0  0  0  2  0  2  0 | * *  *  *  *  *  * 18  *  * | 0 0 0 0 1  0 1 0
x(xo)o .(..). .(..). .(..).&#xr & ♦  3  3 |  1  0  3  4 1 0 | 0  0 0  1  0  0  1  0  1  2 | * *  *  *  *  *  *  * 36  * | 0 0 0 0 0  1 1 0
.(..). o(xo)x .(..). .(..).&#xr & ♦  3  3 |  0  1  4  3 0 1 | 0  0 0  0  1  1  0  1  0  2 | * *  *  *  *  *  *  *  * 36 | 0 0 0 0 0  1 0 1
----------------------------------+-------+-----------------+-----------------------------+-----------------------------+-----------------
x(..).3o(..). x(..).3o(..).     & ♦  9  0 |  9  9  0  0 0 0 | 3  9 3  0  0  0  0  0  0  0 | 3 3  0  0  0  0  0  0  0  0 | 2 * * * *  * * *
x(x.). .(..). x(o.).3o(o.).&#x  & ♦  6  2 |  3  6  6  0 1 0 | 0  3 2  3  0  6  0  0  0  0 | 0 1  3  0  2  0  0  0  0  0 | * 6 * * *  * * *
.(..). o(x.). x(o.).3o(o.).&#x  & ♦  3  2 |  0  3  6  0 0 1 | 0  0 1  0  3  6  0  0  0  0 | 0 0  0  3  2  0  0  0  0  0 | * * 6 * *  * * *
x(.o).3o(.o). x(.x). .(..).&#x  & ♦  6  2 |  6  3  0  6 0 1 | 2  3 0  0  0  0  6  3  0  0 | 1 0  0  0  0  2  3  0  0  0 | * * * 6 *  * * *
x(.o).3o(.o). .(..). o(.x).&#x  & ♦  3  2 |  3  0  0  6 1 0 | 1  0 0  0  0  0  6  0  3  0 | 0 0  0  0  0  2  0  3  0  0 | * * * * 6  * * *
x(xo)o .(..). x(ox)o .(..).&#xr & ♦  5  4 |  2  2  6  6 1 1 | 0  1 0  2  1  2  2  2  1  4 | 0 0  1  0  0  0  1  0  2  2 | * * * * * 18 * *
x(xo)o .(..). .(..). o(ox)x&#xr   ♦  4  4 |  2  0  4  8 2 0 | 0  0 0  2  0  0  4  0  4  4 | 0 0  0  0  0  0  0  2  4  0 | * * * * *  * 9 *
.(..). o(xo)x x(ox)o .(..).&#xr   ♦  4  4 |  0  2  8  4 0 2 | 0  0 0  0  4  4  0  2  0  4 | 0 0  0  2  0  0  0  0  0  4 | * * * * *  * * 9

† – the hull of that compound could be used here instead; that is the bihexagonal tegum xo3xo ox3ox&#zq, the tegum product of 2 x3x.
```

```x(uo)x x(ox)o3o(oo)o3o(ox)x&#xt   → both heights = sqrt(3/8) = 0.612372
(tepe || pseudo (u-line, perp co)-compound † || inv tepe)

o(..). o(..).3o(..).3o(..).     & | 16 *  * ♦ 1  3  1  3  0 |  3  3  3  3  6  3  3 0 0 | 3 1  3  6  3  3  3  1  9 | 1 1 3  3 1  4  3
.(o.). .(o.).3.(o.).3.(o.).       |  * 2  * ♦ 0  0  8  0  0 |  0  0 12  0  0  0 12 0 0 | 0 0  8  0  0  0  0  0 24 | 0 2 0  0 0  8  6
.(.o). .(.o).3.(.o).3.(.o).       |  * * 12 ♦ 0  0  0  4  4 |  0  0  0  2  8  8  2 2 2 | 0 0  0  4  4  4  8  4  8 | 0 0 2  4 2  4  4
----------------------------------+---------+---------------+--------------------------+--------------------------+-----------------
x(..). .(..). .(..). .(..).     & |  2 0  0 | 8  *  *  *  * |  3  0  0  3  0  0  0 0 0 | 3 0  0  6  3  0  0  0  0 | 1 0 3  3 1  0  0
.(..). x(..). .(..). .(..).     & |  2 0  0 | * 24  *  *  * |  1  2  1  0  2  0  0 0 0 | 2 1  2  2  0  2  1  0  2 | 1 1 2  1 0  2  1
o(o.). o(o.).3o(o.).3o(o.).&#x  & |  1 1  0 | *  * 16  *  * |  0  0  3  0  0  0  3 0 0 | 0 0  3  0  0  0  0  0  9 | 0 1 0  0 0  4  3
o(.o). o(.o).3o(.o).3o(.o).&#x  & |  1 0  1 | *  *  * 48  * |  0  0  0  1  2  2  1 0 0 | 0 0  0  2  2  1  2  1  4 | 0 0 1  2 1  2  2
.(..). .(.x). .(..). .(..).     & |  0 0  2 | *  *  *  * 24 |  0  0  0  0  2  2  0 1 1 | 0 0  0  1  1  2  4  2  2 | 0 0 1  2 1  2  2
----------------------------------+---------+---------------+--------------------------+--------------------------+-----------------
x(..). x(..). .(..). .(..).     & |  4 0  0 | 2  2  0  0  0 | 12  *  *  *  *  *  * * * | 2 0  0  2  0  0  0  0  0 | 1 0 2  1 0  0  0
.(..). x(..).3o(..). .(..).     & |  3 0  0 | 0  3  0  0  0 |  * 16  *  *  *  *  * * * | 1 1  1  0  0  1  0  0  0 | 1 1 1  0 0  1  0
.(..). x(o.). .(..). .(..).&#x  & |  2 1  0 | 0  1  2  0  0 |  *  * 24  *  *  *  * * * | 0 0  2  0  0  0  0  0  2 | 0 1 0  0 0  2  1
x(.o). .(..). .(..). .(..).&#x  & |  2 0  1 | 1  0  0  2  0 |  *  *  * 24  *  *  * * * | 0 0  0  2  2  0  0  0  0 | 0 0 1  2 1  0  0
.(..). x(.x). .(..). .(..).&#x  & |  2 0  2 | 0  1  0  2  1 |  *  *  *  * 48  *  * * * | 0 0  0  1  0  1  1  0  1 | 0 0 1  1 0  1  1
.(..). .(..). .(..). o(.x).&#x  & |  1 0  2 | 0  0  0  2  1 |  *  *  *  *  * 48  * * * | 0 0  0  0  1  0  1  1  1 | 0 0 0  1 1  1  1
o(oo)o o(oo)o3o(oo)o3o(oo)o&#xt   |  2 1  1 | 0  0  2  2  0 |  *  *  *  *  *  * 24 * * | 0 0  0  0  0  0  0  0  4 | 0 0 0  0 0  2  2
.(..). .(.x).3.(.o). .(..).     & |  0 0  3 | 0  0  0  0  3 |  *  *  *  *  *  *  * 8 * | 0 0  0  0  0  2  0  2  0 | 0 0 1  0 1  2  0
.(..). .(.x). .(..). .(.x).       |  0 0  4 | 0  0  0  0  4 |  *  *  *  *  *  *  * * 6 | 0 0  0  0  0  0  4  0  0 | 0 0 0  2 0  0  2
----------------------------------+---------+---------------+--------------------------+--------------------------+-----------------
x(..). x(..).3o(..). .(..).     & ♦  6 0  0 | 3  6  0  0  0 |  3  2  0  0  0  0  0 0 0 | 8 *  *  *  *  *  *  *  * | 1 0 1  0 0  0  0
.(..). x(..).3o(..).3o(..).     & ♦  4 0  0 | 0  6  0  0  0 |  0  4  0  0  0  0  0 0 0 | * 4  *  *  *  *  *  *  * | 1 1 0  0 0  0  0
.(..). x(o.).3o(o.). .(..).&#x  & ♦  3 1  0 | 0  3  3  0  0 |  0  1  3  0  0  0  0 0 0 | * * 16  *  *  *  *  *  * | 0 1 0  0 0  1  0
x(.o). x(.x). .(..). .(..).&#x  & ♦  4 0  2 | 2  2  0  4  1 |  1  0  0  2  2  0  0 0 0 | * *  * 24  *  *  *  *  * | 0 0 1  1 0  0  0
x(.o). .(..). .(..). o(.x).&#x  & ♦  2 0  2 | 1  0  0  4  1 |  0  0  0  2  0  2  0 0 0 | * *  *  * 24  *  *  *  * | 0 0 0  1 1  0  0
.(..). x(.x).3o(.o). .(..).&#x  & ♦  3 0  3 | 0  3  0  3  3 |  0  1  0  0  3  0  0 1 0 | * *  *  *  * 16  *  *  * | 0 0 1  0 0  1  0
.(..). x(.x). .(..). o(.x).&#x  & ♦  2 0  4 | 0  1  0  4  4 |  0  0  0  0  2  2  0 0 1 | * *  *  *  *  * 24  *  * | 0 0 0  1 0  0  1
.(..). .(..). o(.o).3o(.x).&#x  & ♦  1 0  3 | 0  0  0  3  3 |  0  0  0  0  0  3  0 1 0 | * *  *  *  *  *  * 16  * | 0 0 0  0 1  1  0
.(..). x(ox)o .(..). .(..).&#xt & ♦  3 1  2 | 0  1  3  4  1 |  0  0  1  0  1  1  2 0 0 | * *  *  *  *  *  *  * 48 | 0 0 0  0 0  1  1
----------------------------------+---------+---------------+--------------------------+--------------------------+-----------------
x(..). x(..).3o(..).3o(..).     & ♦  8 0  0 | 4 12  0  0  0 |  6  8  0  0  0  0  0 0 0 | 4 2  0  0  0  0  0  0  0 | 2 * *  * *  *  *
.(..). x(o.).3o(o.).3o(o.).&#x  & ♦  4 1  0 | 0  6  4  0  0 |  0  4  6  0  0  0  0 0 0 | 0 1  4  0  0  0  0  0  0 | * 4 *  * *  *  *
x(.o). x(.x).3o(.o). .(..).&#x  & ♦  6 0  3 | 3  6  0  6  3 |  3  2  0  3  6  0  0 1 0 | 1 0  0  3  0  2  0  0  0 | * * 8  * *  *  *
x(.o). x(.x). .(..). o(.x).&#x  & ♦  4 0  4 | 2  2  0  8  4 |  1  0  0  4  4  4  0 0 1 | 0 0  0  2  2  0  2  0  0 | * * * 12 *  *  *
x(.o). .(..). o(.o).3o(.x).&#x  & ♦  2 0  3 | 1  0  0  6  3 |  0  0  0  3  0  6  0 1 0 | 0 0  0  0  3  0  0  2  0 | * * *  * 8  *  *
.(..). x(ox)o3o(oo)o .(..).&#xt & ♦  4 1  3 | 0  3  4  6  3 |  0  1  3  0  3  3  3 1 0 | 0 0  1  0  0  1  0  1  3 | * * *  * * 16  *
.(..). x(ox)o .(..). o(ox)x&#xt   ♦  4 1  4 | 0  2  4  8  4 |  0  0  2  0  4  4  4 0 1 | 0 0  0  0  0  0  2  0  4 | * * *  * *  * 12

† – the hull of that compound could be used here instead; that is the tegum uo ox3oo3ox&#zq, the tegum product of u-line and co
```

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