| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 586.1 | One try follows | STAR::BRANDENBERG | Civilization is the progress toward a society of privacy. | Wed Sep 24 1986 20:49 | 6 |
|
Since the four tetrahedra won't cover two of the faces, I would
add an extension from each connection/vertex to the center of the
face in which it lies.
Monty
|
| 586.2 | Eh? | 26205::YARBROUGH | | Thu Sep 25 1986 12:43 | 3 |
| That's not at all clear. Each vertex is part of three faces; each
edge is part of two faces. I can't understand what you are trying
to describe.
|
| 586.3 | | CLT::GILBERT | eager like a child | Thu Sep 25 1986 13:39 | 14 |
| Note that there are two distinct ways of assigning those 4 "/\_"
shapes to edges:
aaaaaaaaaac aaaaaaaaaad
ab cc ab dd
a b c c a b d d
a b c c a b d d
a bbbbbbbbbbb a bcccccccccc
acccdcccccc b adddbdddddd c
a d d b a b c c
a d d b a b c c
ad db ab cc
ddddddddddd bbbbbbbbbbc
|
| 586.4 | how I long for graphics | CACHE::MARSHALL | beware the fractal dragon | Thu Sep 25 1986 13:53 | 27 |
| .----------.
/ /| a b
.----------/ | .----------.
| | | |
| | | | d
| | / | /
| |/ |/
`----------' '
c
connect: a-c,b-d,a-d to form the tetrahedron. Notice that half of
the front face of the cube is the triangle a-b-c, similarly half
the right face is triangle b-c-d. But the top surface (and the bottom
surface) are not contained at all (except at two points).
as I understand .1, disconnect the line a-d. Now place point 'e' in
the center of the top surface, and point 'f' in the center of the
bottom surface. Now, draw lines a-e,e-f,f-d. also, b-e, c-f, a-f,
d-e. this results in an octohedron.
I think this shape does meet the requirements of the puzzle.
/
( ___
) ///
/
|
| 586.5 | Exactly | STAR::BRANDENBERG | Civilization is the progress toward a society of privacy. | Thu Sep 25 1986 14:37 | 1 |
|
|
| 586.6 | Here's a mental image | 26205::YARBROUGH | | Thu Sep 25 1986 16:59 | 6 |
| Right! One way of visualizing this construction is to run an imaginary
rubber band from the top center of the cube: to a corner, down the edge, to
the bottom center, and back up an adjacent edge to the top center. This
outlines one quarter of the cube. Now rotate the top by 90 degrees and you
have the figure of .4. There are also several other solutions; I like
this one.
|
| 586.7 | | CLT::GILBERT | eager like a child | Fri Oct 03 1986 04:15 | 1 |
| Does the same 'extension' work for the other edge assignment given in .3?
|
| 586.8 | Two kinds of /\_'s | MODEL::YARBROUGH | | Fri Oct 03 1986 11:42 | 14 |
| > Does the same 'extension' work for the other edge assignment given in .3?
No. The 'other' (left) alternative in .3 does not conform to the problem
definition in .0, since in that diagram not all the /\_'s are congruent;
two are left-handed, two are right-handed.
In case you need a definition: pick up a /\_ by the middle segment so the
ends hang down with one end close to you. If the nearest bend is to the
left it is left-handed. Viewed from above:
Left Right
/ \
\ /
/ \
|