| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
That was fun. Try this one: a 3-d solid has 6 faces, 12 edges, 8 corners and two of the faces are hexagons. Describe the solid. Lynn Yarbrough
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 215.1 | HARE::STAN | Sat Jan 26 1985 00:17 | 7 | ||
Since two planes meet in a line, the two hexagons can't have more than 2 vertices in common. This would give your solid at least 2 X 6 - 2 = 10 vertices, which is more than the 8 you specify. Thus the solid does not exist unless it has unusual attributes, like coplanar faces. | |||||
| 215.2 | TURTLE::GILBERT | Sat Jan 26 1985 06:49 | 2 | ||
Topologically, there's no problem with the two hexagons having more than two vertices in common. | |||||
| 215.3 | LATOUR::AMARTIN | Sat Jan 26 1985 12:45 | 10 | ||
But geometrically there is a big problem. How can two distinct plane hexagons share more than two points without becoming coplanar? I assume that the two hexagons are supposed to be plane figures, because if the faces don't have to be planar polygons, and the edges don't have to become straight lines, the problem changes from discrete to continuous. (Does anyone want to write a program which enumerates all of the possible solids which fit these descriptions, looking for matches? Looks like we might see some Lisp or Prolog programs, instead of Teco and DCL). /AHM | |||||
| 215.4 | METOO::YARBROUGH | Fri Feb 08 1985 17:11 | 22 | ||
Here it is. Nobody said it had to be convex... it's a trianglular pyramid
wth a notch cut in one edge. - Lynn Yarbrough
^
/|\
/ | \
/ | \
/ | \
/ | \
/ / \ \
/ / \ \
/ /_____\ \
/.....\...../.....\
\ \ / /
\ \ / /
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
v
| |||||