tritep

Acronym	tritep (alt: dycufbil)
Name	(line-)triangle-tegum prism, triangular-bipyramidal prism, dyadic cupofastegia biluna
Lace city in approx. ASCII-art	x o x o x x x o
Dihedral angles	at {4} between trip and trip (equatorial): arccos(-7/9) = 141.057559° at {3} between tete and trip: 90° at {4} between trip and trip (tropal): arccos(1/3) = 70.528779°
Face vector	10, 23, 21, 8
Confer	more general: n-cufbil

Incidence matrix according to Dynkin symbol

xx yo ox3oo&#zx   → height = 0   (y = sqrt(8/3) = 1.632993)

o. o. o.3o.     | 4 * | 1  3 0 0 | 3  3 0 | 3 1
.o .o .o3.o     | * 6 | 0  2 1 2 | 2  4 2 | 4 2
----------------+-----+----------+--------+----
x. .. .. ..     | 2 0 | 2  * * * | 3  0 0 | 3 0
oo oo oo3oo&#x  | 1 1 | * 12 * * | 1  2 0 | 2 1
.x .. .. ..     | 0 2 | *  * 3 * | 2  0 2 | 4 0
.. .. .x ..     | 0 2 | *  * * 6 | 0  2 1 | 2 1
----------------+-----+----------+--------+----
xx .. .. ..&#x  | 2 2 | 1  2 1 0 | 6  * * | 2 0
.. .. ox ..&#x  | 1 2 | 0  2 0 1 | * 12 * | 1 1
.x .. .x ..     | 0 4 | 0  0 2 2 | *  * 3 | 2 0
----------------+-----+----------+--------+----
xx .. ox ..&#x  ♦ 2 4 | 1  4 2 2 | 2  2 1 | 6 *
.. yo ox3oo&#zx ♦ 2 3 | 0  6 0 3 | 0  6 0 | * 2

x(xx)x o(ox)o&#xt   → height(1,2) = height(2,3) = sqrt(2/3) = 0.816497
(line || pseudo trip || line)

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

or
o(..). o(..).     & | 4 * * | 1 1 2 0 0 0 0 | 1 2 1 2 0 0 | 1 2 1
.(o.). .(o.).       | * 2 * | 0 2 0 1 2 0 0 | 2 0 0 4 2 0 | 0 4 1
.(.o). .(.o).       | * * 4 | 0 0 2 0 1 1 1 | 0 2 2 2 1 1 | 2 2 2
--------------------+-------+---------------+-------------+------
x(..). .(..).     & | 2 0 0 | 2 * * * * * * | 1 2 0 0 0 0 | 1 2 0
o(o.). o(o.).&#x  & | 1 1 0 | * 4 * * * * * | 1 0 0 2 0 0 | 0 2 1
o(.o). o(.o).&#x  & | 1 0 1 | * * 8 * * * * | 0 1 1 1 0 0 | 1 1 1
.(x.). .(..).       | 0 2 0 | * * * 1 * * * | 2 0 0 0 2 0 | 0 4 0
.(oo). .(oo).&#x    | 0 1 1 | * * * * 4 * * | 0 0 0 2 1 0 | 0 2 1
.(.x). .(..).       | 0 0 2 | * * * * * 2 * | 0 2 0 0 1 1 | 2 2 0
.(..). .(.x).       | 0 0 2 | * * * * * * 2 | 0 0 2 0 0 1 | 2 0 1
--------------------+-------+---------------+-------------+------
x(x.). .(..).&#x  & | 2 2 0 | 1 2 0 1 0 0 0 | 2 * * * * * | 0 2 0
x(.x). .(..).&#x  & | 2 0 2 | 1 0 2 0 0 1 0 | * 4 * * * * | 1 1 0
.(..). o(.x).&#x  & | 1 0 2 | 0 0 2 0 0 0 1 | * * 4 * * * | 1 0 1
o(oo). o(oo).&#x  & | 1 1 1 | 0 1 1 0 1 0 0 | * * * 8 * * | 0 1 1
.(xx). .(..).&#x    | 0 2 2 | 0 0 0 1 2 1 0 | * * * * 2 * | 0 2 0
.(.x). .(.x).       | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * 1 | 2 0 0
--------------------+-------+---------------+-------------+------
x(.x). o(.x).&#x  & ♦ 2 0 4 | 1 0 4 0 0 2 2 | 0 2 2 0 0 1 | 2 * *
x(xx). .(..).&#x  & ♦ 2 2 2 | 1 2 2 1 2 1 0 | 1 1 0 2 1 0 | * 4 *
.(..). o(ox)o&#x  & ♦ 2 1 2 | 0 2 4 0 2 0 1 | 0 0 2 4 0 0 | * * 2

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