This 110-faced polyhedron has, in addition to the eight regular dodecagons, six rectangles, and 96 triangles. I made it using Stella 4d, a program you can try for free, as a demo version, at http://www.software3d.com/Stella.php. I wish I could remember how I made it!
Fortunately, I have many friends who are more knowledgeable than I, when it comes to mathematics. Perhaps one of them will be able to solve this mystery.
Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.
This particular symmetrohedron features twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.
Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.
This particular symmetrohedron features 12 faces which are regular heptagons, and 8 faces which are regular hexagons. The irregular faces are 12 isosceles triangles, 24 isosceles trapezoids, and 6 rectangles, for a total of 62 faces. It has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.
The twenty faces of this polyhedron are six small blue squares, six interpenetrating, larger red squares, and eight irregular, interpenetrating yellow hexagons. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php. The squares are easy to find, but it can be a challenge to see the yellow hexagons. In the .gif below, all of the yellow faces but one are hidden, which should make it easier to see where the hexagons are positioned, relative to the squares.
I made these using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
I made these .gifs using Stella 4d, software you can try for yourself — free — at http://www.software3d.com/Stella.php.
I made these .gifs using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
I made these .gifs using Stella 4d: Polyhedron Navigator, which you can try for free at this website.
In the compound above, the yellow hexagons are not quite regular, which is why I’m calling the yellow-and-orange polyhedron a truncation of the icosahedron, rather than simply the truncated icosahedron. I stumbled upon it while playing with Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.
What is a cube? That’s a simple question, and I thought it had a simple answer . . . until I took on the project of building cubes with Lux Blox. Lux can be bought at this website, but one thing you won’t find there, or in shipments of Lux, are directions. This was a little frustrating at first, but I understand it now: the makers of Lux don’t want directions getting in the way of customers’ creativity.
A cube has six square faces. This is the six-piece Lux model based on that statement.
This first cube model is interesting, but it is also severely limited. Lux Blox connect at their edges, and all edges in this model are already used, joining one face to another. The model has no openings where more can be attached, and added to it.
Next, I made a cube out of Lux Blox which is open, in the sense that more Lux Blox can be attached to it. It also has an edge length of two.
Besides the openness of this model to new attachments, it also has another characteristic the smaller cube did not have: it can be stretched. If you take two opposite corners of this model and gently pull them away from each other, here’s what you get:
Stretching a cube in this manner creates a six-faced rhombic polyhedron known as a parallelopiped.
The third cube model I’ve built of Lux Blox uses Lux Trigons in addition to the normal square-based Lux Blox.
In this model, the black pieces in the center are the Lux Trigons — twelve of them, occupying the positions of twelve of the twenty faces of an icosahedron. The other eight faces are where the orange triangles (or triangular prisms, if you prefer) are attached. The orange triangles mark the eight corners of a cube. This model has pyritohedral symmetry — the symmetry of a volleyball — as I hope this last picture, a close-up of this third type of cube, helps to illustrate.
