A
dodecahedron, one of the "Platonic solids" of classic
geometry, is bounded by twelve regular pentagons. What would it
be like to live inside a dodecahedron?
We
could build a recreation room in this shape, say with each edge 14
feet long. One of the pentagons would be the floor and another
ceiling. But the ceiling would be more than 30 feet above the
floor, wasting a lot of space.
So
I made a paper model (below) to show how mirrors could be used to
achieve the same effect in onequarter the volume. The floor is
again a pentagon 14 feet on a side. On four of its five sides,
the room has outwardsloping walls consisting of halfpentagons.
Because these walls are not vertical, ordinary swinging doors might
not be practical; the doors would be more like hatches. Perhaps
their thresholds could be three feet outside the
pentagon. Or access to the room could be through its floor via
spiral staircases from the level below; I've drawn threequarter
circles to indicate the tops of these staircases.
(TEXT
CONTINUED BELOW)
The
four wall edges that you see across the top of this picture would
meet a large ceiling mirror (not shown). The mirror would slope
up at an angle of about 28° from the horizontal. At its
high point, the red line, this mirror would intersect at right angles
a large wall mirror inclined about 28° from the vertical.
That mirror would meet the walls at the left and right of this
picture and the floor at the bottom. Because of the slope of
the wall mirror, headroom would be limited on the near side of the
floor; the faint dashed line marks the end of the usable floor area.
The
edges of the pentagons and halfpentagons (black lines on the model)
would be illuminated. Reflected in the mirrors above, these
bars of light would form the image of a complete dodecahedron.
Party on!
