Acronym	traf, K-4.6
Name	triangular antifastegium, triangle oct wedge, {3} || gyro trip, {3} || oct, (vertex-) diminished rap
Segmentochoron display / VRML	⭳
Circumradius	sqrt(3/5) = 0.774597
Lace city in approx. ASCII-art	x3o x3o o3x
	o x x o x x o o
Lace hyper city in approx. ASCII-art	o o o x x x
Dihedral angles	at {4} between squippy and trip:   arccos[-1/sqrt(6)] = 114.094843° at {3} between oct and tet:   arccos(-1/4) = 104.477512° at {3} between squippy and tet:   arccos(-1/4) = 104.477512° at {3} between oct and oct:   arccos(1/4) = 75.522488° at {3} between oct and squippy:   arccos(1/4) = 75.522488° at {3} between oct and trip:   arccos(sqrt[3/8]) = 52.238756°
Face vector	9, 24, 24, 9
Confer	segmentochora family: n-af   n/d-af   uniform relative: rap   related segmentochora: bidrap   variations: xo xo3ox&#q   facetings: reduced( 3/2-af )   general polytopal classes: antifastegia   segmentochora   lace simplices
External links

Incidence matrix according to Dynkin symbol

xoo3oxx&#x   → height(1,2) = height(1,3) = sqrt(2/3) = 0.816497
               height(2,3) = 1
( {3} || (dual {3} || dual {3}) )

o..3o..    | 3 * * ♦ 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 3 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o3..o    | * * 3 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
-----------+-------+-------------+-------------------+----------
x.. ...    | 2 0 0 | 3 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 6 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | * * * 3 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo3.oo&#x | 0 1 1 | * * * * 3 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | * * * * * 3 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------+-------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 3 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 3 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3 * * * * | 0 1 0 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 6 * * * | 0 0 1 1 0
.o.3.x.    | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 3 * | 0 0 0 1 1
..o3..x    | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------+-------------------+----------
xo.3ox.&#x ♦ 3 3 0 | 3 6 0 3 0 0 | 1 3 3 0 0 0 1 0 0 | 1 * * * *
x.o3o.x&#x ♦ 3 0 3 | 3 0 6 0 0 3 | 1 0 0 3 3 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 3 * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 3 *
.oo3.xx&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 0 1 3 1 | * * * * 1

xo3ox ox&#x   → height = sqrt(5/12) = 0.645497
({3} || gyro trip)

o.3o. o.    | 3 * ♦ 2  4 0 0 | 1 4 2 2 0 0 | 2 2 1 0
.o3.o .o    | * 6 | 0  2 2 1 | 0 1 2 2 1 2 | 1 1 2 1
------------+-----+----------+-------------+--------
x. .. ..    | 2 0 | 3  * * * | 1 2 0 0 0 0 | 2 1 0 0
oo3oo oo&#x | 1 1 | * 12 * * | 0 1 1 1 0 0 | 1 1 1 0
.. .x ..    | 0 2 | *  * 6 * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x    | 0 2 | *  * * 3 | 0 0 0 2 0 2 | 0 1 2 1
------------+-----+----------+-------------+--------
x.3o. ..    | 3 0 | 3  0 0 0 | 1 * * * * * | 2 0 0 0
xo .. ..&#x | 2 1 | 1  2 0 0 | * 6 * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0  2 1 0 | * * 6 * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0  2 0 1 | * * * 6 * * | 0 1 1 0
.o3.x ..    | 0 3 | 0  0 3 0 | * * * * 2 * | 1 0 0 1
.. .x .x    | 0 4 | 0  0 2 2 | * * * * * 3 | 0 0 1 1
------------+-----+----------+-------------+--------
xo3ox ..&#x ♦ 3 3 | 3  6 3 0 | 1 3 3 0 1 0 | 2 * * *
xo .. ox&#x ♦ 2 2 | 1  4 0 1 | 0 2 0 2 0 0 | * 3 * *
.. ox ox&#x ♦ 1 4 | 0  4 2 2 | 0 0 2 2 0 1 | * * 3 *
.o3.x .x    ♦ 0 6 | 0  0 6 3 | 0 0 0 0 2 3 | * * * 1

(xx)(oo) (xo)(ox)&#x   → height = sqrt(5/12) = 0.645497
(trip || dual {3})

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

{3} || oct   → height = sqrt(5/8) = 0.790569

o..3o..    | 3 * * ♦ 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0
.o.3.o.    | * 3 * | 0 2 0 2 1 0 | 0 1 2 0 0 2 1 2 0 | 1 0 1 2 1
..o3..o    | * * 3 | 0 0 2 0 1 2 | 0 0 0 1 2 2 0 2 1 | 0 1 1 2 1
-----------+-------+-------------+-------------------+----------
x.. ...    | 2 0 0 | 3 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 6 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
... .x.    | 0 2 0 | * * * 3 * * | 0 0 1 0 0 0 1 1 0 | 1 0 0 1 1
.oo3.oo&#x | 0 1 1 | * * * * 3 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 2 1
... ..x    | 0 0 2 | * * * * * 3 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
-----------+-------+-------------+-------------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 3 * * * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 3 * * * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 3 * * * * * | 0 1 1 0 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3 * * * * | 0 1 0 1 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 6 * * * | 0 0 1 1 0
.o.3.x.    | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 1 * * | 1 0 0 0 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 3 * | 0 0 0 1 1
..o3..x    | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 | 0 1 0 0 1
-----------+-------+-------------+-------------------+----------
xo.3ox.&#x ♦ 3 3 0 | 3 6 0 3 0 0 | 1 3 3 0 0 0 1 0 0 | 1 * * * *
x.o3o.x&#x ♦ 3 0 3 | 3 0 6 0 0 3 | 1 0 0 3 3 0 0 0 1 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 3 * *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 0 1 0 1 2 0 1 0 | * * * 3 *
.oo3.xx&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 0 1 3 1 | * * * * 1

(ox)(xo) (xo)(xo)&#x   → height = sqrt(5/8) = 0.790569
(tet || squippy)

(o.)(..) (o.)(..)     | 2 * * * | 1 2 2 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 | 1 1 2 1 0 0
(.o)(..) (.o)(..)     | * 2 * * ♦ 0 2 0 1 2 1 0 0 0 | 2 1 2 0 0 1 2 1 0 0 0 | 1 2 1 0 1 0
(..)(o.) (..)(o.)     | * * 4 * | 0 0 1 0 1 0 1 1 1 | 0 0 1 1 1 1 1 0 1 1 1 | 0 1 1 1 1 1
(..)(.o) (..)(.o)     | * * * 1 ♦ 0 0 0 0 0 2 0 0 4 | 0 0 0 0 0 0 4 1 0 2 2 | 0 2 0 0 2 1
----------------------+---------+-------------------+-----------------------+------------
(..)(..) (x.)(..)     | 2 0 0 0 | 1 * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 | 1 0 2 1 0 0
(oo)(..) (oo)(..)&#x  | 1 1 0 0 | * 4 * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
(o.)(o.) (o.)(o.)&#x  | 1 0 1 0 | * * 4 * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
(.x)(..) (..)(..)     | 0 2 0 0 | * * * 1 * * * * * | 2 0 0 0 0 0 0 1 0 0 0 | 1 2 0 0 0 0
(.o)(o.) (.o)(o.)&#x  | 0 1 1 0 | * * * * 4 * * * * | 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
(.o)(.o) (.o)(.o)&#x  | 0 1 0 1 | * * * * * 2 * * * | 0 0 0 0 0 0 2 1 0 0 0 | 0 2 0 0 1 0
(..)(x.) (..)(..)     | 0 0 2 0 | * * * * * * 2 * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 0 1 0 1
(..)(..) (..)(x.)     | 0 0 2 0 | * * * * * * * 2 * | 0 0 0 0 1 1 0 0 1 0 1 | 0 0 1 1 1 1
(..)(oo) (..)(oo)&#x  | 0 0 1 1 | * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 1 1 | 0 1 0 0 1 1
----------------------+---------+-------------------+-----------------------+------------
(ox)(..) (..)(..)&#x  | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 | 2 * * * * * * * * * * | 1 1 0 0 0 0
(..)(..) (xo)(..)&#x  | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 | * 2 * * * * * * * * * | 1 0 1 0 0 0
(oo)(o.) (oo)(o.)&#x  | 1 1 1 0 | 0 1 1 0 1 0 0 0 0 | * * 4 * * * * * * * * | 0 1 1 0 0 0
(o.)(x.) (..)(..)&#x  | 1 0 2 0 | 0 0 2 0 0 0 1 0 0 | * * * 2 * * * * * * * | 0 1 0 1 0 0
(..)(..) (x.)(x.)&#x  | 2 0 2 0 | 1 0 2 0 0 0 0 1 0 | * * * * 2 * * * * * * | 0 0 1 1 0 0
(..)(..) (.o)(x.)&#x  | 0 1 2 0 | 0 0 0 0 2 0 0 1 0 | * * * * * 2 * * * * * | 0 0 1 0 1 0
(.o)(oo) (.o)(oo)&#x  | 0 1 1 1 | 0 0 0 0 1 1 0 0 1 | * * * * * * 4 * * * * | 0 1 0 0 1 0
(.x)(.o) (..)(..)&#x  | 0 2 0 1 | 0 0 0 1 0 2 0 0 0 | * * * * * * * 1 * * * | 0 2 0 0 0 0
(..)(x.) (..)(x.)     | 0 0 4 0 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * 1 * * | 0 0 0 1 0 1
(..)(xo) (..)(..)&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 0 2 | * * * * * * * * * 2 * | 0 1 0 0 0 1
(..)(..) (..)(xo)&#x  | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * 2 | 0 0 0 0 1 1
----------------------+---------+-------------------+-----------------------+------------
(ox)(..) (xo)(..)&#x  ♦ 2 2 0 0 | 1 4 0 1 0 0 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 | 1 * * * * *
(ox)(xo) (..)(..)&#xr ♦ 1 2 2 1 | 0 2 2 1 2 2 1 0 2 | 1 0 2 1 0 0 2 1 0 1 0 | * 2 * * * *  cycle (ABDC)
(..)(..) (xo)(x.)&#x  ♦ 2 1 2 0 | 1 2 2 0 2 0 0 1 0 | 0 1 2 0 1 1 0 0 0 0 0 | * * 2 * * *
(o.)(x.) (x.)(x.)&#x  ♦ 2 0 4 0 | 1 0 4 0 0 0 2 2 0 | 0 0 0 2 2 0 0 0 1 0 0 | * * * 1 * *
(..)(..) (.o)(xo)&#x  ♦ 0 1 2 1 | 0 0 0 0 2 1 0 1 2 | 0 0 0 0 0 1 2 0 0 0 1 | * * * * 2 *
(..)(xo) (..)(xo)&#x  ♦ 0 0 4 1 | 0 0 0 0 0 0 2 2 4 | 0 0 0 0 0 0 0 0 1 2 2 | * * * * * 1

xoo&#x || oxx&#x   → height = sqrt(5/8) = 0.790569
(tet || squippy)

o..      ...    | 2 * * * * * | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 0 0 0
.o.      ...    | * 1 * * * * ♦ 0 2 0 0 0 1 1 2 0 0 0 0 0 0 0 | 1 2 2 0 0 0 0 0 1 2 1 0 0 0 0 0 0 | 1 2 1 0 0 1 0 0
..o      ...    | * * 1 * * * ♦ 0 0 2 0 0 1 0 0 1 2 0 0 0 0 0 | 0 2 0 1 2 0 0 0 1 0 0 2 1 0 0 0 0 | 1 2 0 1 0 0 1 0
...      o..    | * * * 1 * * ♦ 0 0 0 0 0 0 1 0 1 0 2 2 0 0 0 | 0 0 0 0 0 0 0 0 1 2 0 2 0 1 2 1 0 | 0 2 0 0 0 1 1 1
...      .o.    | * * * * 2 * | 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 | 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 | 0 1 0 1 1 0 1 1
...      ..o    | * * * * * 2 | 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 | 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 | 0 1 1 0 1 1 0 1
----------------+-------------+-------------------------------+-----------------------------------+----------------
x..      ...    | 2 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 1 0 0 0
oo.&#x   ...    | 1 1 0 0 0 0 | * 2 * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0
o.o&#x   ...    | 1 0 1 0 0 0 | * * 2 * * * * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 0
o..    || .o.    | 1 0 0 0 1 0 | * * * 2 * * * * * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 1 0 0 0
o..    || ..o    | 1 0 0 0 0 1 | * * * * 2 * * * * * * * * * * | 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0
.oo&#x   ...    | 0 1 1 0 0 0 | * * * * * 1 * * * * * * * * * | 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 1 2 0 0 0 0 0 0
.o.    || o..    | 0 1 0 1 0 0 | * * * * * * 1 * * * * * * * * | 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 | 0 2 0 0 0 1 0 0
.o.    || ..o    | 0 1 0 0 0 1 | * * * * * * * 2 * * * * * * * | 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 0 1 0 0
..o    || o..    | 0 0 1 1 0 0 | * * * * * * * * 1 * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 | 0 2 0 0 0 0 1 0
..o    || .o.    | 0 0 1 0 1 0 | * * * * * * * * * 2 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 | 0 1 0 1 0 0 1 0
...      oo.&#x | 0 0 0 1 1 0 | * * * * * * * * * * 2 * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 | 0 1 0 0 0 0 1 1
...      o.o&#x | 0 0 0 1 0 1 | * * * * * * * * * * * 2 * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 1 0 0 0 1 0 1
...      .x.    | 0 0 0 0 2 0 | * * * * * * * * * * * * 1 * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 | 0 0 0 1 1 0 1 1
...      .oo&#x | 0 0 0 0 1 1 | * * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 | 0 1 0 0 1 0 0 1
...      ..x    | 0 0 0 0 0 2 | * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 | 0 0 1 0 1 1 0 1
----------------+-------------+-------------------------------+-----------------------------------+----------------
xo.&#x   ...    | 2 1 0 0 0 0 | 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0
ooo&#x   ...    | 1 1 1 0 0 0 | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
oo.&#x || ..o    | 1 1 0 0 0 1 | 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0
x.o&#x   ...    | 2 0 1 0 0 0 | 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 1 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0
o.o&#x || .o.    | 1 0 1 0 1 0 | 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * 2 * * * * * * * * * * * * | 0 1 0 1 0 0 0 0
x..    || .x.    | 2 0 0 0 2 0 | 1 0 0 2 0 0 0 0 0 0 0 0 1 0 0 | * * * * * 1 * * * * * * * * * * * | 0 0 0 1 1 0 0 0
o..    || .oo&#x | 1 0 0 0 1 1 | 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 | * * * * * * 2 * * * * * * * * * * | 0 1 0 0 1 0 0 0
x..    || ..x    | 2 0 0 0 0 2 | 1 0 0 0 2 0 0 0 0 0 0 0 0 0 1 | * * * * * * * 1 * * * * * * * * * | 0 0 1 0 1 0 0 0
.oo&#x || o..    | 0 1 1 1 0 0 | 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 | * * * * * * * * 1 * * * * * * * * | 0 2 0 0 0 0 0 0
.o.    || o.o&#x | 0 1 0 1 0 1 | 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 | * * * * * * * * * 2 * * * * * * * | 0 1 0 0 0 1 0 0
.o.    || ..x    | 0 1 0 0 0 2 | 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 | * * * * * * * * * * 1 * * * * * * | 0 0 1 0 0 1 0 0
..o    || oo.&#x | 0 0 1 1 1 0 | 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | * * * * * * * * * * * 2 * * * * * | 0 1 0 0 0 0 1 0
..o    || .x.    | 0 0 1 0 2 0 | 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 | * * * * * * * * * * * * 1 * * * * | 0 0 0 1 0 0 1 0
...      ox.&#x | 0 0 0 1 2 0 | 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 0 1 1
...      ooo&#x | 0 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 | * * * * * * * * * * * * * * 2 * * | 0 1 0 0 0 0 0 1
...      o.x&#x | 0 0 0 1 0 2 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * * * * * 1 * | 0 0 0 0 0 1 0 1
...      .xx&#x | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * * * * * * 1 | 0 0 0 0 1 0 0 1
----------------+-------------+-------------------------------+-----------------------------------+----------------
xoo&#x   ...    ♦ 2 1 1 0 0 0 | 1 2 2 0 0 1 0 0 0 0 0 0 0 0 0 | 1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * *
ooo&#x || ooo&#x ♦ 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 | 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 | * 2 * * * * * *
xo.&#x || ..x    ♦ 2 1 0 0 0 2 | 1 2 0 0 2 0 0 2 0 0 0 0 0 0 1 | 1 0 2 0 0 0 0 1 0 0 1 0 0 0 0 0 0 | * * 1 * * * * *
x.o&#x || .x.    ♦ 2 0 1 0 2 0 | 1 0 2 2 0 0 0 0 0 2 0 0 1 0 0 | 0 0 0 1 2 1 0 0 0 0 0 0 1 0 0 0 0 | * * * 1 * * * *
x..    || .xx&#x ♦ 2 0 0 0 2 2 | 1 0 0 2 2 0 0 0 0 0 0 0 1 2 1 | 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 | * * * * 1 * * *
.o.    || o.x&#x ♦ 0 1 0 1 0 2 | 0 0 0 0 0 0 1 2 0 0 0 2 0 0 1 | 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 1 0 | * * * * * 1 * *
..o    || ox.&#x ♦ 0 0 1 1 2 0 | 0 0 0 0 0 0 0 0 1 2 2 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 | * * * * * * 1 *
...      oxx&#x ♦ 0 0 0 1 2 2 | 0 0 0 0 0 0 0 0 0 0 2 2 1 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 1 | * * * * * * * 1

ooxx oxox&#xr   → height(1,2) = height(2,4) = height(3,4) = sqrt(3)/2 = 0.866025
                  height(1,4) = height(2,3) = 1/sqrt(2) = 0.707107

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

xoxoxo&#xr   → all consecutive pairwise heights = sqrt(3)/2 = 0.866025
               all alternating pairwise heights = 1
               Note: these lengths show that this cycle is not flat, rather it is wobbling up and down!

o.....     & | 6 * | 1  2 2 0 | 2 2 2 1 1 0 | 2 1 1 1
.o....     & | * 3 ♦ 0  4 0 2 | 2 2 0 0 4 1 | 1 2 0 2
-------------+-----+----------+-------------+--------
x.....     & | 2 0 | 3  * * * | 2 0 2 0 0 0 | 2 0 1 1
oo....&#x  & | 1 1 | * 12 * * | 1 1 0 0 1 0 | 1 1 0 1
o.o...&#x  & | 2 0 | *  * 6 * | 0 1 1 1 0 0 | 1 1 1 0
.o.o..&#x  & | 0 2 | *  * * 3 | 0 0 0 0 2 1 | 0 2 0 1
-------------+-----+----------+-------------+--------
xo....&#x  & | 2 1 | 1  2 0 0 | 6 * * * * * | 1 0 0 1
ooo...&#x  & | 2 1 | 0  2 1 0 | * 6 * * * * | 1 1 0 0
x.x...&#x  & | 4 0 | 2  0 2 0 | * * 3 * * * | 1 0 1 0
o.o.o.&#x    | 3 0 | 0  0 3 0 | * * * 2 * * | 0 1 1 0
.ooo..&#x  & | 1 2 | 0  2 0 1 | * * * * 6 * | 0 1 0 1
.o.o.o&#x    | 0 3 | 0  0 0 3 | * * * * * 1 | 0 2 0 0
-------------+-----+----------+-------------+--------
xox...&#x  & ♦ 4 1 | 2  4 2 0 | 2 2 1 0 0 0 | 3 * * *
oooooo&#x    ♦ 3 3 | 0  6 3 3 | 0 3 0 1 3 1 | * 2 * *
x.x.x.&#x    ♦ 6 0 | 3  0 6 0 | 0 0 3 2 0 0 | * * 1 *
.oxo..&#x  & ♦ 2 2 | 1  4 0 1 | 2 0 0 0 2 0 | * * * 3

o(xx)o x(ox)o&#xt   → height(1,2) = height(3,4) = 1/sqrt(12) = 0.288675
                      height(1,3) = height(2,3) = height(2,4) = 1/sqrt(3) = 0.577350
                      height(1,23) = height(23,4) = sqrt(5/12) = 0.645497

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