Acronym	...
Name	Dohány synagoge polyhedron, Tabakgasse polyhedron
	© ©
Circumradius	sqrt(7/6) = 1.080123
Face vector	16, 28, 14
External links

Theodor Herzl in 1850 described it as "Tabakgasse polyhedron", because, as a lantern's basic form, it is being found within the Dohány synagoge of Budapest. It shall be noted that the name of that "shul" is and was based on the adjoining street's name, which formally was known as Tabakgasse.

Note that both, the base squares as well as the lateral hexagons, are regular ones! They just have different side lengths. The sides of the square have unit size x, while those of the hexagon have a somewhat smaller size y = q/h = sqrt(2/3) = 0.816497. (All edges of size q within the below lace tower description are pseudo ones.)

This polyhedron well could be face inscribed into a square prism with sides q, q, and 2y, where that ratio then is 2y/q = qy = u/h = 2/sqrt(3) = 1.154701.

Incidence matrix according to Dynkin symbol

xoox4oqqo&#yt   → outer heights = 1/sqrt(6) = 0.408248
                  inner height = y = sqrt(2/3) = 0.816497

o...4o...     | 4 * * * | 2 2 0 0 0 | 1 2 1 0 0
.o..4.o..     | * 4 * * | 0 2 1 0 0 | 0 1 2 0 0
..o.4..o.     | * * 4 * | 0 0 1 2 0 | 0 0 2 1 0
...o4...o     | * * * 4 | 0 0 0 2 2 | 0 0 1 2 1
--------------+---------+-----------+----------
x... ....     | 2 0 0 0 | 4 * * * * | 1 1 0 0 0
oo..4oo..&#y  | 1 1 0 0 | * 8 * * * | 0 1 1 0 0
.oo.4.oo.&#y  | 0 1 1 0 | * * 4 * * | 0 0 2 0 0
..oo4..oo&#y  | 0 0 1 1 | * * * 8 * | 0 0 1 1 0
...x ....     | 0 0 0 2 | * * * * 4 | 0 0 0 1 1
--------------+---------+-----------+----------
x...4o...     | 4 0 0 0 | 4 0 0 0 0 | 1 * * * *  x-{4}
xo.. ....&#y  | 2 1 0 0 | 1 2 0 0 0 | * 4 * * *
.... oqqo&#yt | 1 2 2 1 | 0 2 2 2 0 | * * 4 * *  y-{6}
..ox ....&#y  | 0 0 1 2 | 0 0 0 2 1 | * * * 4 *
...x4...o     | 0 0 0 4 | 0 0 0 0 4 | * * * * 1  x-{4}

or
o...4o...     & | 8 * | 2  2 0 | 1 2 1
.o..4.o..     & | * 8 | 0  2 1 | 0 1 2
----------------+-----+--------+------
x... ....     & | 2 0 | 8  * * | 1 1 0
oo..4oo..&#y  & | 1 1 | * 16 * | 0 1 1
.oo.4.oo.&#y    | 0 2 | *  * 4 | 0 0 2
----------------+-----+--------+------
x...4o...     & | 4 0 | 4  0 0 | 2 * *  x-{4}
xo.. ....&#y  & | 2 1 | 1  2 0 | * 8 *
.... oqqo&#yt   | 2 4 | 0  4 2 | * * 4  y-{6}