The Mystery of Mirror Systems in Kaleidoscopes Unfolded

Equilateral TriangleEquilateral TriangleThree equal sides
Three equal angles, always 60°
Scalene TriangleRight TriangleNo equal sides
No equal angles, one 90°
Isosceles TriangleIsosceles TriangleTwo equal sides
Two equal angles
Scalene TriangleIsosceles Right TriangleTwo equal sides
Two equal angles,  one 90°
  • The number and angles of mirrors inside kaleidoscopes determine the shape of the image you will see in a kaleidoscope.

2 Mirror Systems

  • A kaleidoscope with two mirrors will produce a round mandala and the angles of the mirrors will determine the number of points that you will see inside.
Angle of MirrorsFoldsPoints
90 Degrees42
60 Degrees63
45 Degrees84
36 Degrees105
30 Degrees126
25.7 Degrees147
22.5 Degrees168
20 Degrees189
18 Degrees2010
16.3 Degrees2211
15 Degrees2412
12 Degrees3015
10 Degrees3618
9 Degrees4020
6 Degrees6030
5 Degrees7236

We handmake our Color Spirit Kaleidoscopes using a 2 mirror system mirrors and a black matte board as the third side

our 2 mirrors are set at 30 degrees producing a 6 point interior mandala Image.

3 Mirror Systems

On the other hand, the most popular kaleidoscopes contain three mirrors, which will produce an entire field of patterns that are triangular in shape, The angles inside can be equilateral (three sides are all the same), or isosceles (two sides are the same, but a third is different, or a 30/60/90 degree triangle.

Be sure to check out the images shown on the page. A three-mirror system inside a kaleidoscope should equal 180 degrees, but any form of triangle. The images inside are continuous and rather honeycomb-like patterns. There are numerous examples of these on my website. One can see the equal sides reflecting the equilateral triangular mirrors inside on “Plum Blossom”:

3 mirror interior image

30 60 90 3 Mirror Systems

Likewise, you can see several examples of a kaleidoscope with an isosceles configuration. One rather inexpensive model has been a top seller for all ages, and is seen here Another especially enjoyable image is the 30/60/90 degree designed kaleidoscope. Such a kaleidoscope contains three types of symmetry: fourfold (from the 90 degree angle) sixfold (from the 60 degree angle) and 12-fold (from the 30 degree angle.)

3 Mirror Tapered Mirror Systems

this is a fun and unique interior image as it produces a 3 d Globe like image

4 Mirror Systems

There can be four mirrors inside a kaleidoscope, and are not seen as much as the 2 and 3 mirror kaleidoscopes. So, the number and differing angles of mirrors are determining the image inside! That is worth repeating, because it is one of the reasons that kaleidoscopes are revered and collected by many people. As mentioned in the first paragraph, there can even be four mirrors inside, which typically produces a long and narrow, square or rectangular image inside. An example of a four mirror can only be seen, but not purchased since it is a vintage 1985 model, by going to my website, The vintage kaleidoscope, “Brass 4 mirror” (era 1985) is by Apries La Pluie of France and is discontinued and not in stock, but is a wonderful example of a 4 mirror.

Polyangular Mirror Systems

Perhaps the most perfect symmetry and best images appear inside two-mirror kaleidoscopes when the angle between the mirrors divides equally into 360 degrees. Hopefully the following makes sense! Degrees Symmetry Points 60 6-fold 3 45 8-fold 4 36 10-fold 5 30 12-fold 6 22.5 16-fold 8 20 18-fold 9 18 20-fold 10 15 24-fold 12 Now, imagine if the designer can make one mirror of a two-mirror kaleidoscope change angles! It has been done! It’s called a polyangular (meaning many angles) kaleidoscope and is most elaborate and satisfying. A wide range of symmetrical patterns can be produced in a polyangular kaleidoscope! Steven Gray made many of them in the 2010s, and they are now quite collectable.

Unusual Mirror Systems and Creative use of reflective materials

As the mirror system is the heart of the kaleidoscope it is no wonder many artists have come up with some fun and verry different non traditional mirror systems.

So the sky is the limit here limited only to your creativity and available reflective materials.

Here is one artists Work Marc Tickle who through out his career produced many different and exciting Mirror systems

Artist Steven Gray was another artist pushing the creativity of Mirror sytems in his artwork.

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