Brynk

Players	2-99
Playtime	15-30 mins
Suggested Age	7 and up
Publisher	Winning Moves Games (USA)
Additional Info	192500/brynk https://boardgamegeek.com/boardgame/192500/brynk/forums/63

From the publisher's website:

Will you be able to place your pieces on the teeter-tottering base and get it to stay? Or will you upset the balance and watch as it all comes crashing down in front of you?

Players take turns adding pieces (triangles, squares, or pentagons) onto the Brynk tower by hooking them onto any available slot. If one or more pieces falls off the tower during a player's turn, that player is eliminated from the game and play continues to the left; however, if the entire tower falls over or all of the pieces fall off, the game ends immediately and the last player who successfully placed a piece on the tower is the winner!