Category:Concertina cube
The concertina cube is an integral polyhedron based on a 4×4×4 cube. It is created by truncating the edges and vertices of the cube that are part of its Petrie hexagon (see here).
Its skeleton is a Hasse diagram. Each of the vertices corresponds to a formula with 3 different variables in first-order logic, and each edge to one of the implications between them.
Each pair of opposite vertices corresponds to one of the weak orderings of 3 elements.
Elements: (compare row 3 of A300700)
- 26 vertices (2 · orderedBell(3))
- 42 edges
- 18 faces: 6 concertina squares, 6 rectangles, 6 rhombi
Surface: hexagon rectangle rhombus total
Volume: A300697(3) = 52 (12 cut away from 4×4×4=64)
The coordinates are permutations of these points: (list)
(0, 0, 0) | (4, 4, 4) | ranks 0 / 6 |
(0, 0, 2) | (2, 4, 4) | ranks 1 / 5 |
(0, 1, 3) | (1, 3, 4) | ranks 2 / 4 |
(0, 3, 3) | (1, 1, 4) | rank 3 |
Subcategories
This category has the following 6 subcategories, out of 6 total.
C
- Concertina cube; graph (6 F)
T
Media in category "Concertina cube"
This category contains only the following file.
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Concertina cube.stl 5,120 × 2,880; 2 KB