pattern for the lilac square with treble tatting

Only text, no visual diagram. Pattern is original, @Antonina Caruso 2018.

For the sequence of steps for tatting a tds, refer to this post: treble tatting - ideas
or watch this video in YouTube: https://youtu.be/ra0NnlqR0oA

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UPDATE: Please refer to the page "Treble Tatting Stitch - Summary" - https://ninettacaruso.blogspot.com/p/blog-page_95.html for any info about treble tatting stitches, thank you.
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For this pattern, load 2 shuttles CTM. Otherwise, each round needs cut and tie and restart afresh, avoiding two split rings and one split chain. There are 3 more split rings in third round that can't be avoided. There are both normal joins and lock joins.

Abbreviations:
ds=double stitch; p=picot
tds=treble tatting stitch (it starts always with a vsp, then it's never mentioned);
R=ring; Ch=chain; vsp=very small picot;
SR=split ring (text is in the form SR: first side/second side);
SCh=split chain (text is in the form SCh: first side/second side);
⭐= don't reverse here, if you do direct tatting for chains

Pattern:
First round:
R: 4ds, p, 3ds, 4tds, vsp, 3ds, p, 4ds: close and don't reverse work.
R: 4ds, join to last p in previous R, 3ds, 4tds, vsp, 3ds, p, 4ds: close and don't reverse work.
Tat another ring exactly the same.
SR: 4ds, join to last p in previous R, 3ds, 4tds / 4ds,  join to first p in first R, 3ds; close and do not reverse work.

Second round:
SR (start first side with the second shuttle and leave a very short bare thread -same height of the tds- before starting the second side of the SR): 6ds / 6ds, join the vsp of the first tds of the first ring in first round, 6ds; close and reverse work (⭐)
(*) Ch: 3ds, p, 3ds, p, 3ds; reverse work (⭐)
R: 4ds, join the next vsp between first and second tds of ring of previous round, 4ds; close and reverse work (⭐)
Ch: 2ds, p, 2ds;  reverse work (⭐)
R: 4ds, join the next vsp between second and third tds of ring of previous round, 4ds; close and reverse work (⭐)
Ch: 2ds, p, 2ds;  reverse work (⭐)
R: 4ds, join the next vsp between third and fourth tds of ring of previous round, 4ds; close and reverse work (⭐)
Ch: 3ds, p, 3ds, p, 3ds; reverse work (⭐)
R: 6ds, join last vsp after the fourth tds of ring of previous round, 6ds, join the vsp of the first tds of the next ring in first round, 6ds, close and reverse work (⭐)
Repeat from the chain (*) another 2 times, then:
Ch: 3ds, p, 3ds, p, 3ds; reverse work (⭐)
R: 4ds, join the next vsp between first and second tds of ring of previous round, 4ds; close and reverse work (⭐)
Ch: 2ds, p, 2ds;  reverse work (⭐)
R: 4ds, join the next vsp between second and third tds of ring of previous round, 4ds; close and reverse work (⭐)
Ch: 2ds, p, 2ds;  reverse work (⭐)
R: 4ds, join the next vsp between third and fourth tds of ring of previous round, 4ds; close and reverse work (⭐)
SCh:  3ds, p, 3ds / 3ds; reverse work (⭐) and turn work upside down

Third round:
(core thread of previous round becomes the "ball" thread, and vice versa)
(**) Ch: 4ds; lock join to the second p of first chain (*) of previous round
Ch: 1ds, 9tds, vsp, 1ds; lock join to the first p of next chain (*) of previous round
Ch: 4ds; lock join to the second p of chain (*) of previous round; reverse work (⭐)
SR:  3ds /3ds, p, 3ds; close and normal join to the first p of next chain (*) of previous round; close and reverse work (⭐); 
Repeat from the chain (**) another 3 times, except the very last SR that is:
SR: 3ds, join to the starting point of third round, 3ds / 3ds; close and reverse work (⭐);

Fourth round:
Climb up with a mock picot.
(***) Ch: 3ds, p, 3ds, p, 3ds; lock join to the first vsp of the first tds of the long chain of previous round
Ch: 3ds, join to last p of previous chain, 3ds, p, 3ds;  reverse work (⭐);
R: 3ds, skip one vsp and join the next vsp between second and third tds of ring of the long chain of previous round, 3ds; close and reverse work (⭐)
Ch: 3ds, p, 3ds;  reverse work (⭐);
R: 3ds, skip one vsp below and join the next vsp between forth and fifth tds of ring of the long chain of previous round, 3ds; close and reverse work (⭐)
Ch: 2ds, p, 2ds;  reverse work (⭐);
R: 3ds, join the next vsp between fifth and sixth tds of ring of the long chain of previous round, 3ds; close and reverse work (⭐)
Ch: 3ds, p, 3ds;  reverse work (⭐);
R: 3ds, skip one vsp below and join the next vsp between seventh and eighth tds of ring of the long chain of previous round, 3ds; close and reverse work (⭐)
Ch: 3ds, p, 3ds, p, 3ds; lock join to the vsp just after the last tds of the long chain of previous round
Ch: 3ds, join to last p of previous chain, 3ds, p, 3ds; lock join to the picot of the SR of previous round.
Repeat from the chain (***) 3 times more.

Use your favourite way to tie and cut ends. 
Ciao,
Ninetta