The 3-pieces twist opening burr Three is deeply in love with a 6-pieces slide opening burr called Six.
Three's type of connection is the pieces intersecting through each crossing piece.
To release a piece a crossing piece has to be rotated. If slided it would cut off it self or the crossing pieces. And the twisting piece need tangential space to rotate.
Six's type of connection is two adjacent pieces embracing another piece in each end. To be released, an embracing piece has to give the notches to the pieces that it holds. If it were made twisting to release the embraced piece, yet that piece would need to be released by the other embracing piece.
Still, Three has a plan how to interest Six. Three has got it's pieces lengthened to measure with Six's pieces and so be able to embrace them:
Three is now on it's way to meet with Six:
Six heart jumped when it saw how Three had extended itself to match pieces. Six was delighted of how handsome Three looked. Three told it had 8 units added to it's pieces and asked if it's feelings were answered:
Six told it had 8 units extra notches hidden! Six then moved 3 of it's pieces to express the feelings it had for Three.
Three saw it was a perfect match and it instantly proposed to Six to marry it:
Six said "Yes, I will marry you, your notches matches my notches perfectly!"
And off they went to the puzzler to get married together.
After they been built together to a new semi symmetrical 9-piece solid burr, Three promised Six; "I will always have a piece ready to slide when you need". Six promised Three; "I will always have a piece to twist when you need me to in the puzzle". They were very happy together: