¶ Cube (1)
Index Entry
Cube:
"If the cube is an entity it has 18 structural lines. If a dodecahedron is an entity, it has 32 vertexes, 60 faces, and 90 structural lines. (The primes 5 and 3 show up here to produce our icosahedral friend 15.)
"Whenever we refer to an entity it has to be structurally valid and therefore it has to be triangulated. This does not throw topology out.
"A nonstructurally-triangulated cube exists only by self-deceptive topological accounting: someone shows you a paper or sheet-metal cube and says, ‘Here is a structurally stable cube without any face diagonalling.’ And you say what do you call that sheet-metal or paper which is occupying the square faces without which the cube would not exist. The sheet-metal or paper does diagonal the square but overdoes it redundantly.
"A blackboard drawing of a 12-line cube is only an imaginary, impossible structure which could not exist in this part of Universe. It could temporarily hold its shape in gravity low regions of space or in another, imaginary Universe.
¶ Citations
- RBF to EJA, 3200 Idaho, DC, 20 Feb '72, re-written 22 Feb.
