Cut a Cube into six identical pieces each having nine edges !

3 hours ago, Commander said:

Cut a Cube into four identical pieces each having nine edges !

Please note it is four pieces and not six ! Error regretted !!

Edited August 18, 20232 yr by Commander

Spoiler

 

Also all the faces of the pieces must be TRIANGLES  !

Sorry I forgot to mention this !

 

Two triangular pyramids, not necessarily equilateral, attached at a base make a shape with triangular faces and nine edges.

Trying to imagine how to put four of these shapes together.

ChatGPT asked me to tell you this:

Spoiler

It's not possible to cut a cube into four identical pieces, each with 9 edges and triangular faces. A cube has 12 edges and 6 square faces. In order to create pieces with triangular faces, you would need to further subdivide the cube's faces. However, doing so will result in more than 9 edges on each piece.

If you're looking to create four identical pieces with triangular faces and 9 edges, you would need a different shape or object that meets these criteria, as it cannot be achieved with a cube.

Just passing the message 😉

Spoiler

I think your shape is a "diamond" AKA two tetrahedrons put together.  Put 8 tetra in a cube so each tetra shares a face with another, and you have filled cube with four diamonds.  I can't quite see it, atm.

ETA -guess I didn't need to hide that, seeing now Genadys post.

Edited August 18, 20232 yr by TheVat

Spoiler

Start at a corner, add the 3 nearest corners, and the center of the cube. Those make up the 5 points of the "diamond"...

 

1 hour ago, md65536 said:

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Start at a corner, add the 3 nearest corners, and the center of the cube. Those make up the 5 points of the "diamond"...

 

Thank you. Here I've sketched it. The four shapes are 1-0, 2-0, 3-0, and 4-0, where I've numbered the opposite vertices of each:

Spoiler

 

5 hours ago, Genady said:

ChatGPT asked me to tell you this:

  Reveal hidden contents

It's not possible to cut a cube into four identical pieces, each with 9 edges and triangular faces. A cube has 12 edges and 6 square faces. In order to create pieces with triangular faces, you would need to further subdivide the cube's faces. However, doing so will result in more than 9 edges on each piece.

If you're looking to create four identical pieces with triangular faces and 9 edges, you would need a different shape or object that meets these criteria, as it cannot be achieved with a cube.

Just passing the message 😉

You need to chop of four corners with an equilateral triangle as the base with sides of diagonals
Four of them 

That leaves a tetrahedron in the middle 
We need to cut it in four equal parts with each equilateral triangular base (four of them) and apex meeting at the center of the cube

The four earlier cut pieces (cut for the sake of explanation) are merged with equal area bases of the four pieces of the tetrahedron

Need to cut like that !