Welz Umbrella shapes - 4 sided shapes

I want to set out to categorize these knuckle (Umbrella) glass pieces in a new way; by their geometry and technique. I am categorizing them as 4-sided, 6-sided 8-sided and multi-sided. I am also not covering baskets or lampshades.

Franz Welz created some beautiful shapes (after 1925) but none seem as labor intensive as these Umbrella shapes. They would have started with a base color, powder and (or) glass confetti, then blown it into a mold (to create the pattern) then applied a rim, transferring the pontil to the base (holding pontil) then finally working the upper portion with shears and tongs.

I am open to any other glass blowing theories but whatever the specific technical aspects are- these types were much harder shapes to produce than the regular "cut from the top" types.
Most of these pieces (seem to) have 5 types of protrusions- so I assume three types of tools were used; these tools were used to expand the shape from the inside (tongs).

The protrusion I will refer to:
1. Thorn- single sharp protrusion
2. Elbow- a right angle curve protrusion

3. Claw- 4 circular protrusions
4. Spine- 4 linear protrusions

Thank you to collectors who's pictures you see here, my intention was not to steal anything but to do side-by-side studies to benefit future collectors and to add appreciation to the glass blowing masters of this company.

1. Fan vases with with different two different feet; I hate to think of these as fan vases but in truth they are very narrow and can only displayed from the profile. The 3-ball piece has a pontil and mold marks all the way to the rim. The decor for both vases is Lines and Dots. Elbow protrusions were used to expand the inside of the vase

2. Box vases with two different feet; one square the other round. The decors are Bi-color tango (confetti over tango base) and Lines with Confetti. Decors are Lines with confetti and Lines and Dots. Spine protrusions were used to expand the inside of the vase

3. Trumpet vases in two shape dimensions (with two types of feet)
Elbow and thorn protrusions were used to expand the inside of the vase

4. Square rim shape (bowl and vase). Both of these pieces have an "embossed" texture coming from being blown into a mold. The decor is Confetti on Tango. Thorn and Elbow protrusions were used to expand the inside of the vase. on a side note- if you look at my 8-sided post you will see the same shape can be either 8-sided if you consider the interior or 4-sided if you consider only the rim... "phew"