Acronym	rap (old: rip, alt.: tetaoct), tet || oct, K-4.5
Name	rectified pentachoron, pyrorectichoron, tetrahedral cupola, vertex figure of hin, tetrahedron atop octahedron, Gosset polytope 02,1
Segmentochoron display
Cross sections	©
Circumradius	sqrt(3/5) = 0.774597
Inradius wrt. tet	3/sqrt(40) = 0.474342
Inradius wrt. oct	1/sqrt(10) = 0.316228
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o o3o3o . o3o . o o . o3o . o3o3o 1 o3x3o3o o3x3o . oct first o3x . o {3} first o . o3o vertex first . x3o3o tet first 2 x3o3o . opposite tet x3o . x x . x3o vertex figure . o3x3o opposite oct 3   o3o . o opposite vertex o . o3x opposite {3}
Lace city in approx. ASCII-art	o3o x3o -- tet x3o o3x -- oct
	x o o x -- tet o o x x o o -- oct \ \ +-- {3} \ +------- gyro trip +------------ point
Lace hyper city in approx. ASCII-art	©   o o x o layer of tet o o o x layer of tet o o o layer of oct o o o o x x layer of oct o o o layer of oct
	©   o point x x x trip o o o dual {3}
Volume	11 sqrt(5)/96 = 0.256216
Surface	25 sqrt(2)/12 = 2.946278
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: oct tet trip rap 5 5 0 pinnip 5 0 10 firp 0 5 10 )
Dual	o3m3o3o
Dihedral angles	at {3} between oct and tet:   arccos(-1/4) = 104.477512° at {3} between oct and oct:   arccos(1/4) = 75.522488°
Face vector	10, 30, 30, 10
Confer	Grünbaumian relatives: firp+rap+15{4}   2rap   2rap+20tet   related segmentochora: trippy   bidrap   traf   pafirp   fitetaoct   hotetahoct   variations: qo3oq3oo&#x   blends: turap   aurap   ambification: srip   ambification pre-image: pen   general polytopal classes: Wythoffian polychora   segmentochora   fundamental lace prisms   bistratic lace towers   lace simplices   Coxeter-Elte-Gosset polytopes   analogs: rectified simplex rSn   birectified simplex brSn   Gossetic n2,1   rectified Gossetic r(n2,1)   rectified Gossetic r(1n,2)
External links

 ©

A 4D representation of the Petersen graph can be obtained by the vertices and the diagonals of the octs of this polychoron. Even though, the fact that 3 lines then do cross perpendicularily each, happens to be a matter of this representation only. Geometrically, the Petersen graph also is the graph formed by the vertices and edges of the hemi-dodecahedron (eldoe), that is, a dodecahedron where opposite points, lines and faces got identified.

Incidence matrix according to Dynkin symbol

o3x3o3o

. . . . | 10 ♦  6 |  3  6 | 3 2
--------+----+----+-------+----
. x . . |  2 | 30 |  1  2 | 2 1
--------+----+----+-------+----
o3x . . |  3 |  3 | 10  * | 2 0
. x3o . |  3 |  3 |  * 20 | 1 1
--------+----+----+-------+----
o3x3o . ♦  6 | 12 |  4  4 | 5 *
. x3o3o ♦  4 |  6 |  0  4 | * 5

snubbed forms: o3β3o3o

o3x3o3/2o

. . .   . | 10 ♦  6 |  3  6 | 3 2
----------+----+----+-------+----
. x .   . |  2 | 30 |  1  2 | 2 1
----------+----+----+-------+----
o3x .   . |  3 |  3 | 10  * | 2 0
. x3o   . |  3 |  3 |  * 20 | 1 1
----------+----+----+-------+----
o3x3o   . ♦  6 | 12 |  4  4 | 5 *
. x3o3/2o ♦  4 |  6 |  0  4 | * 5

o3x3/2o3o

. .   . . | 10 ♦  6 |  3  6 | 3 2
----------+----+----+-------+----
. x   . . |  2 | 30 |  1  2 | 2 1
----------+----+----+-------+----
o3x   . . |  3 |  3 | 10  * | 2 0
. x3/2o . |  3 |  3 |  * 20 | 1 1
----------+----+----+-------+----
o3x3/2o . ♦  6 | 12 |  4  4 | 5 *
. x3/2o3o ♦  4 |  6 |  0  4 | * 5

o3x3/2o3/2o

. .   .   . | 10 ♦  6 |  3  6 | 3 2
------------+----+----+-------+----
. x   .   . |  2 | 30 |  1  2 | 2 1
------------+----+----+-------+----
o3x   .   . |  3 |  3 | 10  * | 2 0
. x3/2o   . |  3 |  3 |  * 20 | 1 1
------------+----+----+-------+----
o3x3/2o   . ♦  6 | 12 |  4  4 | 5 *
. x3/2o3/2o ♦  4 |  6 |  0  4 | * 5

o3/2x3o3o

.   . . . | 10 ♦  6 |  3  6 | 3 2
----------+----+----+-------+----
.   x . . |  2 | 30 |  1  2 | 2 1
----------+----+----+-------+----
o3/2x . . |  3 |  3 | 10  * | 2 0
.   x3o . |  3 |  3 |  * 20 | 1 1
----------+----+----+-------+----
o3/2x3o . ♦  6 | 12 |  4  4 | 5 *
.   x3o3o ♦  4 |  6 |  0  4 | * 5

o3/2x3o3/2o

.   . .   . | 10 ♦  6 |  3  6 | 3 2
------------+----+----+-------+----
.   x .   . |  2 | 30 |  1  2 | 2 1
------------+----+----+-------+----
o3/2x .   . |  3 |  3 | 10  * | 2 0
.   x3o   . |  3 |  3 |  * 20 | 1 1
------------+----+----+-------+----
o3/2x3o   . ♦  6 | 12 |  4  4 | 5 *
.   x3o3/2o ♦  4 |  6 |  0  4 | * 5

o3/2x3/2o3o

.   .   . . | 10 ♦  6 |  3  6 | 3 2
------------+----+----+-------+----
.   x   . . |  2 | 30 |  1  2 | 2 1
------------+----+----+-------+----
o3/2x   . . |  3 |  3 | 10  * | 2 0
.   x3/2o . |  3 |  3 |  * 20 | 1 1
------------+----+----+-------+----
o3/2x3/2o . ♦  6 | 12 |  4  4 | 5 *
.   x3/2o3o ♦  4 |  6 |  0  4 | * 5

o3/2x3/2o3/2o

.   .   .   . | 10 ♦  6 |  3  6 | 3 2
--------------+----+----+-------+----
.   x   .   . |  2 | 30 |  1  2 | 2 1
--------------+----+----+-------+----
o3/2x   .   . |  3 |  3 | 10  * | 2 0
.   x3/2o   . |  3 |  3 |  * 20 | 1 1
--------------+----+----+-------+----
o3/2x3/2o   . ♦  6 | 12 |  4  4 | 5 *
.   x3/2o3/2o ♦  4 |  6 |  0  4 | * 5

xo3ox3oo&#x   → height = sqrt(5/8) = 0.790569
(tet || oct)

o.3o.3o.    | 4 * ♦ 3  3  0 | 3 3  3 0 0 | 1 3 1 0
.o3.o3.o    | * 6 ♦ 0  2  4 | 0 1  4 2 2 | 0 2 2 1
------------+-----+---------+------------+--------
x. .. ..    | 2 0 | 6  *  * | 2 1  0 0 0 | 1 2 0 0
oo3oo3oo&#x | 1 1 | * 12  * | 0 1  2 0 0 | 0 2 1 0
.. .x ..    | 0 2 | *  * 12 | 0 0  1 1 1 | 0 1 1 1
------------+-----+---------+------------+--------
x.3o. ..    | 3 0 | 3  0  0 | 4 *  * * * | 1 1 0 0
xo .. ..&#x | 2 1 | 1  2  0 | * 6  * * * | 0 2 0 0
.. ox ..&#x | 1 2 | 0  2  1 | * * 12 * * | 0 1 1 0
.o3.x ..    | 0 3 | 0  0  3 | * *  * 4 * | 0 1 0 1
.. .x3.o    | 0 3 | 0  0  3 | * *  * * 4 | 0 0 1 1
------------+-----+---------+------------+--------
x.3o.3o.    ♦ 4 0 | 6  0  0 | 4 0  0 0 0 | 1 * * *
xo3ox ..&#x ♦ 3 3 | 3  6  3 | 1 3  3 1 0 | * 4 * *
.. ox3oo&#x ♦ 1 3 | 0  3  3 | 0 0  3 0 1 | * * 4 *
.o3.x3.o    ♦ 0 6 | 0  0 12 | 0 0  0 4 4 | * * * 1

oxo oxo3oox&#xt   → both heights = sqrt(5/12) = 0.645497
(pt || pseudo trip || dual {3})

o.. o..3o..     | 1 * * ♦ 6 0 0  0 0 | 3 6 0 0 0 0 0 | 3 2 0 0
.o. .o.3.o.     | * 6 * ♦ 1 1 2  2 0 | 1 2 1 2 2 1 0 | 2 1 1 1
..o ..o3..o     | * * 3 ♦ 0 0 0  4 2 | 0 0 0 2 2 4 1 | 1 0 2 2
----------------+-------+------------+---------------+--------
oo. oo.3oo.&#x  | 1 1 0 | 6 * *  * * | 1 2 0 0 0 0 0 | 2 1 0 0
.x. ... ...     | 0 2 0 | * 3 *  * * | 1 0 0 2 0 0 0 | 2 0 1 0
... .x. ...     | 0 2 0 | * * 6  * * | 0 1 1 0 1 0 0 | 1 1 0 1
.oo .oo3.oo&#x  | 0 1 1 | * * * 12 * | 0 0 0 1 1 1 0 | 1 0 1 1
... ... ..x     | 0 0 2 | * * *  * 3 | 0 0 0 0 0 2 1 | 0 0 1 2
----------------+-------+------------+---------------+--------
ox. ... ...&#x  | 1 2 0 | 2 1 0  0 0 | 3 * * * * * * | 2 0 0 0
... ox. ...&#x  | 1 2 0 | 2 0 1  0 0 | * 6 * * * * * | 1 1 0 0
... .x.3.o.     | 0 3 0 | 0 0 3  0 0 | * * 2 * * * * | 0 1 0 1
.xo ... ...&#x  | 0 2 1 | 0 1 0  2 0 | * * * 6 * * * | 1 0 1 0
... .xo ...&#x  | 0 2 1 | 0 0 1  2 0 | * * * * 6 * * | 1 0 0 1
... ... .ox&#x  | 0 1 2 | 0 0 0  2 1 | * * * * * 6 * | 0 0 1 1
... ..o3..x     | 0 0 3 | 0 0 0  0 3 | * * * * * * 1 | 0 0 0 2
----------------+-------+------------+---------------+--------
oxo oxo ...&#xt ♦ 1 4 1 | 4 2 2  4 0 | 2 2 0 2 2 0 0 | 3 * * *
... ox.3oo.&#x  ♦ 1 3 0 | 3 0 3  0 0 | 0 3 1 0 0 0 0 | * 2 * *
.xo ... .ox&#x  ♦ 0 2 2 | 0 1 0  4 1 | 0 0 0 2 0 2 0 | * * 3 *
... .xo3.ox&#x  ♦ 0 3 3 | 0 0 3  6 3 | 0 0 1 0 3 3 1 | * * * 2

o(xx)(oo) o(xo)(ox)&#xt   → both heights = sqrt(5/12) = 0.645497
(pt || pseudo trip || dual {3})

o(..)(..) o(..)(..)     | 1 * * * * ♦ 4 2 0 0 0 0 0 0 0 0 0 | 2 2 4 1 0 0 0 0 0 0 0 0 0 | 1 2 2 0 0 0
.(o.)(..) .(o.)(..)     | * 4 * * * ♦ 1 0 1 1 1 1 1 0 0 0 0 | 1 1 1 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 1 0
.(.o)(..) .(.o)(..)     | * * 2 * * ♦ 0 1 0 0 2 0 0 1 2 0 0 | 0 0 2 1 1 2 0 0 0 0 2 1 0 | 0 2 1 1 0 1
.(..)(o.) .(..)(o.)     | * * * 1 * ♦ 0 0 0 0 0 4 0 0 0 2 0 | 0 0 0 0 0 0 2 2 4 0 0 0 1 | 1 0 0 2 2 0
.(..)(.o) .(..)(.o)     | * * * * 2 ♦ 0 0 0 0 0 0 2 0 2 1 1 | 0 0 0 0 0 2 0 0 2 1 1 2 1 | 0 1 0 2 1 1
------------------------+-----------+-----------------------+---------------------------+------------
o(o.)(..) o(o.)(..)&#x  | 1 1 0 0 0 | 4 * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
o(.o)(..) o(.o)(..)&#x  | 1 0 1 0 0 | * 2 * * * * * * * * * | 0 0 2 1 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0
.(x.)(..) .(..)(..)     | 0 2 0 0 0 | * * 2 * * * * * * * * | 1 0 0 0 0 0 1 0 0 1 0 0 0 | 1 1 0 0 1 0
.(..)(..) .(x.)(..)     | 0 2 0 0 0 | * * * 2 * * * * * * * | 0 1 0 0 1 0 0 1 0 0 0 0 0 | 1 0 1 1 0 0
.(oo)(..) .(oo)(..)&#x  | 0 1 1 0 0 | * * * * 4 * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
.(o.)(o.) .(o.)(o.)&#x  | 0 1 0 1 0 | * * * * * 4 * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 | 1 0 0 1 1 0
.(o.)(.o) .(o.)(.o)&#x  | 0 1 0 0 1 | * * * * * * 4 * * * * | 0 0 0 0 0 1 0 0 1 1 0 0 0 | 0 1 0 1 1 0
.(.x)(..) .(..)(..)     | 0 0 2 0 0 | * * * * * * * 1 * * * | 0 0 0 1 0 0 0 0 0 0 2 0 0 | 0 2 0 0 0 1
.(.o)(.o) .(.o)(.o)&#x  | 0 0 1 0 1 | * * * * * * * * 4 * * | 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 1 0 1 0 1
.(..)(oo) .(..)(oo)&#x  | 0 0 0 1 1 | * * * * * * * * * 2 * | 0 0 0 0 0 0 0 0 2 0 0 0 1 | 0 0 0 2 1 0
.(..)(..) .(..)(.x)     | 0 0 0 0 2 | * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 2 0 1
------------------------+-----------+-----------------------+---------------------------+------------
o(x.)(..) .(..)(..)&#x  | 1 2 0 0 0 | 2 0 1 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 1 1 0 0 0 0
.(..)(..) o(x.)(..)&#x  | 1 2 0 0 0 | 2 0 0 1 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * | 1 0 1 0 0 0
o(oo)(..) o(oo)(..)&#x  | 1 1 1 0 0 | 1 1 0 0 1 0 0 0 0 0 0 | * * 4 * * * * * * * * * * | 0 1 1 0 0 0
o(.x)(..) .(..)(..)&#x  | 1 0 2 0 0 | 0 2 0 0 0 0 0 1 0 0 0 | * * * 1 * * * * * * * * * | 0 2 0 0 0 0
.(..)(..) .(xo)(..)&#x  | 0 2 1 0 0 | 0 0 0 1 2 0 0 0 0 0 0 | * * * * 2 * * * * * * * * | 0 0 1 1 0 0
.(oo)(.o) .(oo)(.o)&#x  | 0 1 1 0 1 | 0 0 0 0 1 0 1 0 1 0 0 | * * * * * 4 * * * * * * * | 0 1 0 1 0 0
.(x.)(o.) .(..)(..)&#x  | 0 2 0 1 0 | 0 0 1 0 0 2 0 0 0 0 0 | * * * * * * 2 * * * * * * | 1 0 0 0 1 0
.(..)(..) .(x.)(o.)&#x  | 0 2 0 1 0 | 0 0 0 1 0 2 0 0 0 0 0 | * * * * * * * 2 * * * * * | 1 0 0 1 0 0
.(o.)(oo) .(o.)(oo)&#x  | 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * 4 * * * * | 0 0 0 1 1 0
.(x.)(.o) .(..)(..)&#x  | 0 2 0 0 1 | 0 0 1 0 0 0 2 0 0 0 0 | * * * * * * * * * 2 * * * | 0 1 0 0 1 0
.(.x)(.o) .(..)(..)&#x  | 0 0 2 0 1 | 0 0 0 0 0 0 0 1 2 0 0 | * * * * * * * * * * 2 * * | 0 1 0 0 0 1
.(..)(..) .(.o)(.x)&#x  | 0 0 1 0 2 | 0 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * 2 * | 0 0 0 1 0 1
.(..)(..) .(..)(ox)&#x  | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * 1 | 0 0 0 2 0 0
------------------------+-----------+-----------------------+---------------------------+------------
o(x.)(o.) o(x.)(o.)&#xt ♦ 1 4 0 1 0 | 4 0 2 2 0 4 0 0 0 0 0 | 2 2 0 0 0 0 2 2 0 0 0 0 0 | 1 * * * * *
o(xx)(.o) .(..)(..)&#xt ♦ 1 2 2 0 1 | 2 2 1 0 2 0 2 1 2 0 0 | 1 0 2 1 0 2 0 0 0 1 1 0 0 | * 2 * * * *
.(..)(..) o(xo)(..)&#x  ♦ 1 2 1 0 0 | 2 1 0 1 2 0 0 0 0 0 0 | 0 1 2 0 1 0 0 0 0 0 0 0 0 | * * 2 * * *
.(..)(..) .(xo)(ox)&#x  ♦ 0 2 1 1 2 | 0 0 0 1 2 2 2 0 2 2 1 | 0 0 0 0 1 2 0 1 2 0 0 1 1 | * * * 2 * *
.(x.)(oo) .(..)(..)&#x  ♦ 0 2 0 1 1 | 0 0 1 0 0 2 2 0 0 1 0 | 0 0 0 0 0 0 1 0 2 1 0 0 0 | * * * * 2 *
.(.x)(.o) .(.o)(.x)&#x  ♦ 0 0 2 0 2 | 0 0 0 0 0 0 0 1 4 0 1 | 0 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * 1

oxoo3xoxo&#xr   → all heights = sqrt(2/3) = 0.816497
({3} || pseudo (dual {3} || pt) || {3})

o...3o...     | 3 * * * ♦ 2 2 1 1 0 0 0 0 | 1 1 2 2 2 1 0 0 0 0 0 | 1 1 1 2 0 0
.o..3.o..     | * 3 * * ♦ 0 2 0 0 2 2 0 0 | 0 2 1 0 2 0 1 2 1 0 0 | 1 0 2 1 1 0
..o.3..o.     | * * 3 * ♦ 0 0 1 0 0 2 2 1 | 0 0 0 0 2 1 0 1 2 1 2 | 0 0 1 2 1 1
...o3...o     | * * * 1 ♦ 0 0 0 3 0 0 0 3 | 0 0 0 3 0 3 0 0 0 0 3 | 0 1 0 3 0 1
--------------+---------+-----------------+-----------------------+------------
.... x...     | 2 0 0 0 | 3 * * * * * * * | 1 0 1 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
oo..3oo..&#x  | 1 1 0 0 | * 6 * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
o.o.3o.o.&#x  | 1 0 1 0 | * * 3 * * * * * | 0 0 0 0 2 1 0 0 0 0 0 | 0 0 1 2 0 0
o..o3o..o&#x  | 1 0 0 1 | * * * 3 * * * * | 0 0 0 2 0 1 0 0 0 0 0 | 0 1 0 2 0 0
.x.. ....     | 0 2 0 0 | * * * * 3 * * * | 0 1 0 0 0 0 1 1 0 0 0 | 1 0 1 0 1 0
.oo.3.oo.&#x  | 0 1 1 0 | * * * * * 6 * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 0 1 1 1 0
.... ..x.     | 0 0 2 0 | * * * * * * 3 * | 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1
..oo3..oo&#x  | 0 0 1 1 | * * * * * * * 3 | 0 0 0 0 0 1 0 0 0 0 2 | 0 0 0 2 0 1
--------------+---------+-----------------+-----------------------+------------
o...3x...     | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 1 0 0 0 0
ox.. ....&#x  | 1 2 0 0 | 0 2 0 0 1 0 0 0 | * 3 * * * * * * * * * | 1 0 1 0 0 0
.... xo..&#x  | 2 1 0 0 | 1 2 0 0 0 0 0 0 | * * 3 * * * * * * * * | 1 0 0 1 0 0
.... x..o&#x  | 2 0 0 1 | 1 0 0 2 0 0 0 0 | * * * 3 * * * * * * * | 0 1 0 1 0 0
ooo.3ooo.&#x  | 1 1 1 0 | 0 1 1 0 0 1 0 0 | * * * * 6 * * * * * * | 0 0 1 1 0 0
o.oo3o.oo&#x  | 1 0 1 1 | 0 0 1 1 0 0 0 1 | * * * * * 3 * * * * * | 0 0 0 2 0 0
.x..3.o..     | 0 3 0 0 | 0 0 0 0 3 0 0 0 | * * * * * * 1 * * * * | 1 0 0 0 1 0
.xo. ....&#x  | 0 2 1 0 | 0 0 0 0 1 2 0 0 | * * * * * * * 3 * * * | 0 0 1 0 1 0
.... .ox.&#x  | 0 1 2 0 | 0 0 0 0 0 2 1 0 | * * * * * * * * 3 * * | 0 0 0 1 1 0
..o.3..x.     | 0 0 3 0 | 0 0 0 0 0 0 3 0 | * * * * * * * * * 1 * | 0 0 0 0 1 1
.... ..xo&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * * * * 3 | 0 0 0 1 0 1
--------------+---------+-----------------+-----------------------+------------
ox..3xo..&#x  ♦ 3 3 0 0 | 3 6 0 0 3 0 0 0 | 1 3 3 0 0 0 1 0 0 0 0 | 1 * * * * *
o..o3x..o&#x  ♦ 3 0 0 1 | 3 0 0 3 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * 1 * * * *
oxo. ....&#x  ♦ 1 2 1 0 | 0 2 1 0 1 2 0 0 | 0 1 0 0 2 0 0 1 0 0 0 | * * 3 * * *
.... xoxo&#xr ♦ 2 1 2 1 | 1 2 2 2 0 2 1 2 | 0 0 1 1 2 2 0 0 1 0 1 | * * * 3 * *
.xo.3.ox.&#x  ♦ 0 3 3 0 | 0 0 0 0 3 6 3 0 | 0 0 0 0 0 0 1 3 3 1 0 | * * * * 1 *
..oo3..xo&#x  ♦ 0 0 3 1 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 1 3 | * * * * * 1

oxoox oxoxo&#xr   → height(1,2) = height(2,3) = height(4,5) = 1/sqrt(2) = 0.707107
                    height(1,5) = height(3,4) = sqrt(3)/2 = 0.866025
(layer 1-3: oct-base, layer 4+5: tet-base)

o.... o....     | 1 * * * * ♦ 4 2 0 0 0 0 0 0 0 0 0 | 2 2 1 4 0 0 0 0 0 0 0 0 0 | 1 2 2 0 0 0
.o... .o...     | * 4 * * * ♦ 1 0 1 1 1 1 1 0 0 0 0 | 1 1 0 1 1 1 1 1 1 1 0 0 0 | 1 1 1 1 1 0
..o.. ..o..     | * * 1 * * ♦ 0 0 0 0 4 0 0 2 0 0 0 | 0 0 0 0 2 2 0 0 4 0 1 0 0 | 1 0 0 2 2 0
...o. ...o.     | * * * 2 * ♦ 0 0 0 0 0 2 0 1 1 2 0 | 0 0 0 0 0 0 1 0 2 2 1 1 2 | 0 1 0 1 2 1
....o ....o     | * * * * 2 ♦ 0 1 0 0 0 0 2 0 0 2 1 | 0 0 1 2 0 0 0 1 0 2 0 2 1 | 0 2 1 0 1 1
----------------+-----------+-----------------------+---------------------------+------------
oo... oo...&#x  | 1 1 0 0 0 | 4 * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
o...o o...o&#x  | 1 0 0 0 1 | * 2 * * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0
.x... .....     | 0 2 0 0 0 | * * 2 * * * * * * * * | 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 1 0 1 0 0
..... .x...     | 0 2 0 0 0 | * * * 2 * * * * * * * | 0 1 0 0 0 1 0 1 0 0 0 0 0 | 1 0 1 0 1 0
.oo.. .oo..&#x  | 0 1 1 0 0 | * * * * 4 * * * * * * | 0 0 0 0 1 1 0 0 1 0 0 0 0 | 1 0 0 1 1 0
.o.o. .o.o.&#x  | 0 1 0 1 0 | * * * * * 4 * * * * * | 0 0 0 0 0 0 1 0 1 1 0 0 0 | 0 1 0 1 1 0
.o..o .o..o&#x  | 0 1 0 0 1 | * * * * * * 4 * * * * | 0 0 0 1 0 0 0 1 0 1 0 0 0 | 0 1 1 0 1 0
..oo. ..oo.&#x  | 0 0 1 1 0 | * * * * * * * 2 * * * | 0 0 0 0 0 0 0 0 2 0 1 0 0 | 0 0 0 1 2 0
..... ...x.     | 0 0 0 2 0 | * * * * * * * * 1 * * | 0 0 0 0 0 0 0 0 0 0 1 0 2 | 0 0 0 0 2 1
...oo ...oo&#x  | 0 0 0 1 1 | * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 1 0 1 1 | 0 1 0 0 1 1
....x .....     | 0 0 0 0 2 | * * * * * * * * * * 1 | 0 0 1 0 0 0 0 0 0 0 0 2 0 | 0 2 0 0 0 1
----------------+-----------+-----------------------+---------------------------+------------
ox... .....&#x  | 1 2 0 0 0 | 2 0 1 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * | 1 1 0 0 0 0
..... ox...&#x  | 1 2 0 0 0 | 2 0 0 1 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * | 1 0 1 0 0 0
o...x .....&#x  | 1 0 0 0 2 | 0 2 0 0 0 0 0 0 0 0 1 | * * 1 * * * * * * * * * * | 0 2 0 0 0 0
oo..o oo..o&#x  | 1 1 0 0 1 | 1 1 0 0 0 0 1 0 0 0 0 | * * * 4 * * * * * * * * * | 0 1 1 0 0 0
.xo.. .....&#x  | 0 2 1 0 0 | 0 0 1 0 2 0 0 0 0 0 0 | * * * * 2 * * * * * * * * | 1 0 0 1 0 0
..... .xo..&#x  | 0 2 1 0 0 | 0 0 0 1 2 0 0 0 0 0 0 | * * * * * 2 * * * * * * * | 1 0 0 0 1 0
.x.o. .....&#x  | 0 2 0 1 0 | 0 0 1 0 0 2 0 0 0 0 0 | * * * * * * 2 * * * * * * | 0 1 0 1 0 0
..... .x..o&#x  | 0 2 0 0 1 | 0 0 0 1 0 0 2 0 0 0 0 | * * * * * * * 2 * * * * * | 0 0 1 0 1 0
.ooo. .ooo.&#x  | 0 1 1 1 0 | 0 0 0 0 1 1 0 1 0 0 0 | * * * * * * * * 4 * * * * | 0 0 0 1 1 0
.o.oo .o.oo&#x  | 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * * 4 * * * | 0 1 0 0 1 0
..... ..ox.&#x  | 0 0 1 2 0 | 0 0 0 0 0 0 0 2 1 0 0 | * * * * * * * * * * 1 * * | 0 0 0 0 2 0
...ox .....&#x  | 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * 2 * | 0 1 0 0 0 1
..... ...xo&#x  | 0 0 0 2 1 | 0 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * 2 | 0 0 0 0 1 1
----------------+-----------+-----------------------+---------------------------+------------
oxo.. oxo..&#xt ♦ 1 4 1 0 0 | 4 0 2 2 4 0 0 0 0 0 0 | 2 2 0 0 2 2 0 0 0 0 0 0 0 | 1 * * * * *
ox.ox .....&#xr ♦ 1 2 0 1 2 | 2 2 1 0 0 2 2 0 0 2 1 | 1 0 1 2 0 0 1 0 0 2 0 1 0 | * 2 * * * *
..... ox..o&#x  ♦ 1 2 0 0 1 | 2 1 0 1 0 0 2 0 0 0 0 | 0 1 0 2 0 0 0 1 0 0 0 0 0 | * * 2 * * *
.xoo. .....&#x  ♦ 0 2 1 1 0 | 0 0 1 0 2 2 0 1 0 0 0 | 0 0 0 0 1 0 1 0 2 0 0 0 0 | * * * 2 * *
..... .xoxo&#xr ♦ 0 2 1 2 1 | 0 0 0 1 2 2 2 2 1 2 0 | 0 0 0 0 0 1 0 1 2 2 1 0 1 | * * * * 2 *
...ox ...xo&#x  ♦ 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 0 0 0 2 2 | * * * * * 1

or
o.... o....     & | 2 * * ♦ 4 2 0 0 0 0 | 2 2 1 4 0 0 0 | 1 2 2 0  A=C
.o... .o...       | * 4 * ♦ 2 0 2 2 0 0 | 2 2 0 2 2 1 0 | 1 2 2 0  B
...o. ...o.     & | * * 4 ♦ 0 1 0 2 1 2 | 0 0 1 2 1 2 3 | 0 3 1 1  D=E
------------------+-------+-------------+---------------+--------
oo... oo...&#x  & | 1 1 0 | 8 * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
o...o o...o&#x  & | 1 0 1 | * 4 * * * * | 0 0 1 2 0 0 0 | 0 2 1 0
.x... .....     & | 0 2 0 | * * 4 * * * | 1 1 0 0 1 0 0 | 1 1 1 0
.o.o. .o.o.&#x  & | 0 1 1 | * * * 8 * * | 0 0 0 1 1 1 0 | 0 2 1 0
..... ...x.     & | 0 0 2 | * * * * 2 * | 0 0 1 0 0 0 2 | 0 2 0 1
...oo ...oo&#x    | 0 0 2 | * * * * * 4 | 0 0 0 0 0 1 2 | 0 2 0 1
------------------+-------+-------------+---------------+--------
ox... .....&#x  & | 1 2 0 | 2 0 1 0 0 0 | 4 * * * * * * | 1 1 0 0
..... ox...&#x  & | 1 2 0 | 2 0 1 0 0 0 | * 4 * * * * * | 1 0 1 0
o...x .....&#x  & | 1 0 2 | 0 2 0 0 1 0 | * * 2 * * * * | 0 2 0 0
oo..o oo..o&#x  & | 1 1 1 | 1 1 0 1 0 0 | * * * 8 * * * | 0 1 1 0
.x.o. .....&#x  & | 0 2 1 | 0 0 1 2 0 0 | * * * * 4 * * | 0 1 1 0
.o.oo .o.oo&#x    | 0 1 2 | 0 0 0 2 0 1 | * * * * * 4 * | 0 2 0 0
...ox .....&#x  & | 0 0 3 | 0 0 0 0 1 2 | * * * * * * 4 | 0 1 0 1
------------------+-------+-------------+---------------+--------
oxo.. oxo..&#xt   ♦ 2 4 0 | 8 0 4 0 0 0 | 4 4 0 0 0 0 0 | 1 * * *
ox.ox .....&#xr & ♦ 1 2 3 | 2 2 1 4 1 2 | 1 0 1 2 1 2 1 | * 4 * *
..... ox..o&#x  & ♦ 1 2 1 | 2 1 1 2 0 0 | 0 1 0 2 1 0 0 | * * 4 *
...ox ...xo&#x    ♦ 0 0 4 | 0 0 0 0 2 4 | 0 0 0 0 0 0 4 | * * * 1