Since computer screens can't display many colors, where can I go to see the full color gamut? I found out recently that computer screens are only able to display a subset of all the colors visible to the human eye. Naturally one of my first questions was what do the other colors look like, but this is one of the few questions that I cannot Google. I have been able to find a few objects around my house that I'm pretty sure have colors that my screen can't display, but I'd like to see the full gamut. I will have to find it IRL, so my question is where can I find it? Is my local library likely to have a picture? I live in Boston so I was thinking I could try the Science Museum or the MIT Museum, but neither seems to have an exhibit on color.
 A: I suppose what you want is to see the full gamut of chromaticity, ignoring luminance. Otherwise you'd have to somehow display a 3D volume of colors.
Unfortunately, even chromaticity gamut isn't easy to display. There's no monitor currently manufactured that would be able to display all the chromaticities of the visible gamut, and no color printer that would be able to help here too.
What are the obstacles? First, the chromaticity gamut is not a polygon. It has a curvy border everywhere except the line of purples (and the line from infrared to yellowish-green 550 nm, where curvature is small), see the following diagram (image source; the colors outside the sRGB gamut are undersaturated to fill the whole shape):

This means that you can't take a finite (or too small) number of primary colors to mix so as to get any other color.
Second, if an approximation of the true curve by a (possibly many-vertex) polygon can satisfy you, there's a problem of finding the necessary light sources. Red and infrared colors of high saturation can be easily obtained by LEDs. But to get really saturated violets, blues, cyans, and especially greens you need lasers. And this can be challenging, depending on how well you want to fill the gamut (some wavelengths are easier to obtain, others are only emitted by very expensive and often energy-inefficient lasers).
So, if you really want to see the whole gamut at once, you'll have to devise something yourself. Maybe make your own laser projector (not too infeasible if you take two mirrors and a set of lasers, and modulate lasers' intensities while the mirrors are rotating).
If not at once, then you just have to mix the laser lights with corresponding intensities shone at some good diffusely reflecting white surface. The hard part is to make the light homogeneous enough so as to not get gradient instead of the color you're trying to display.

Now, there's also the peculiarity that the exact visible color gamut actually varies between people—even those with "standard" trichromacy, i.e. without anomalies. The reasons for this are e.g. yellowing of the eye lens with age and varying pigmentation in the macula of the retina. Moreover, the gamut differs even in different parts of the retina: e.g. for foveal area there's the standard gamut defined by the CIE 1931 Standard Observer that describes the 2° area of the central vision, while for larger part of the macula (10° in the center) there's the CIE 1964 Standard Observer. So in practice, although one can in principle create something that would shine the whole (standard) chromaticity gamut from some surface, it'll likely be missing some small set of colors that you personally could distinguish—due to individual variation of color vision.
A: You can't go anywhere to see the "full color gamut".  There are three types of cone cells on your retina that only see the colors red, green, and blue, which are the same colors that are imprinted into the tiny phosphors on your color TV screen.  Thus, your eye can only see these three colors.
In everyday experience, a particular object will reflect varying amplitudes of red, green, and blue to your retina.  If all of these colors have equal amplitudes, your brain interprets the light reflecting off a given object as "white".  With all other amplitude combinations, your brain will interpret the color as something between red and violet.
A: The colors you can see form (the positive orthant of) a three-dimensional real vector space.  (A color is defined by three real numbers, describing the intensity of stimulation of the three types of cones.)  A computer can display a finite number of colors.   So you'll never get close to displaying the "entire gamut".
On the other hand, you could certainly ask for a computer that can display a set of colors that are "dense" in the sense that for any given color X, there exists a displayable color Y with the property that you can't subjectively notice the difference betweeen X and Y.  How big that set of colors would have to be --- and whether it is greater or less than the number that your computer already displays --- seems like more of a biology question than a physics question.
