3M's rendition of Stewart Coffin's original wooden version called 'Hexsticks' .

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12 pieces     (9 two-notched)  (3 three-notched)

There are three known plastic color versions of the Hectix :
~ all white -- red, white and blue -- and all clear ~
I chose the red, white and blue for this solution -- against a yellowish background -- because the color combination among the pieces themselves and their background, is the easiest to follow when viewing the pictures .
This solution also affords you easy construction of the the puzzle while it rests on a flat surface .

One starts building the Hectix from the bottom up .
All 9 two-notched pieces are used first .

                  Start a tripod base (1,2,3) . . . . .                     . . . . . add three more sticks vertically (4,5,6). . . . .

Add the last 3 sticks at an angle (7,8,9)
~ like the tripod base ~

Arrange the 3 three-notched pieces upside down from step 1 . . .
. . . making sure the 'third notch' on all three is perpendicular to the tripod top .
(this will allow the tripod top to slide down the top of the already-assembled main structure)

The reverse tripod top now settling into the assembled partial structure

Once the tripod top is settled all the way into the puzzle structure -- even though the completed puzzle has a certain 'sloppiness' to it -- the slight inherent looseness of all the pieces from handling shift will cause most of the notch edges to hold the tripod top and keep it from sliding back out, even when the puzzle is turned upside down .