When it comes to the Tefillin Batim, the boxes in which the Parshios / Tefillin Passages are held, there are several different qualities.
The Tefillin Batim need to be made from one piece of skin because the Torah says “ulezikaron bein einecha” “a sign between your eyes” the word sign is in the singular form. Thereby teaching us that the Tefillin box needs to be one sign I.E one piece of skin. There are many ways to construct a Bayis in order that it be one skin.
Peshutos Peshutos: Which literally means simple simple. These Tefillin Batim are made from many pieces of parchment glued together (being that the glue makes it one piece of skin this is not preferred). As well they are generally of poor quality and often Halachicly problematic, and they don’t last very long. I do not sell these Batim.
Peshutos Mehudaros: (Image 1) The upper section of the Tefillin Batim /Box is made from one piece of klaf, but are cut in specific places and can be glued together to become a box, sort of like origami (being that the glue makes it one piece of skin this is still not preferred). Then additional leather is added on to strengthen these Batim. These Batim are better then the Peshutim, because the upper section is from one piece of skin. However, it is still not Mehudar because glue is used to make it “one skin”. These too being that they are made from Klaf which is thin are not very durable typically only last several years.
Dakos: (Image 2) A base is made from thicker hide where glue is used. However afterwards a thin skin such as a goat or shlil/still-born is then stretched over it, so it is covered with one piece of skin. This is considered to be or echod/one solid piece of skin and they are sturdier then the first two types.
Gasos: (Image 3)Are one solid piece of hide from the forehead, face and neck of a thick-skinned animal such as a bull. After a long taning process they are formed and pressed into the desired shape. and then left a year to dry. Theses batim last the longest and are the most durable. No glue is used whatsoever making these Tefillin Batim Mehudar.
Dakos or Gasos?The advantage of Gasos is that they are much more durable, and last a lot longer. However Dakos has the advantage that it can be made from the skin of a still-born, which is more Mehudar for it had not yet entered the world, which represents Severity. Gasos cannot be made from shlil for the skin is too thin.Dakos or Gasos? Do to the questionable Kashrus of Peshutim I do not sell these, however I do have a selection of Mehudorim, Dakos and Gasos. In general I recommend Gasos or Dakos over the Mehudorim For they are made better and will last longer.
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Another aspect of Mehudar/Halachik preference in the Tefillin Batim is if no glue is found between the four compartments of the Shel Rosh. For according to Halacha if you glue leather together it is considered as “one skin”. Based on that premises the Peshutim Mehudaros, are Kosher, but on the same note if there is glue between the four compartments they will lose their status of being their own compartment, and be considered one big compartment with three dividers, and not be Kosher.
However if the glue is less than a quarter of the way up and not on the edges it is Kosher, but a higher level of being Mehudar is that there be no glue in between the compartments whatsoever.
As well it is more Mehudar for the Teffilin to be two thumb widths by two thumb widths, according to Rav Avraham Chaim Naeh it is 4×4 centimeters measuring at the base which is a standard 3.5 on the Ketzizah
The opinion of Chabad Chassidim is that the measurement of 2×2 thumb widths (4×4 centimeters) is going on the Ketzitza (the top part of the box) where the Parshios are held, not on the base of the Tefillin, which is wider. That is why Chabad typically wear larger Tefillin.