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THE HYPERCUBE - THE ROLYGON - HYPERTUBE

The Rhombus

The rhombus was developed to make the effects of such a major re-mapping of space unmistakable. It is a combination of elements, which respond well to pseudoscopic vision, and other elements that intentionally in contrast respond less well.

A transparent rhombus is particularly suitable to demonstrate pseudoscopic effects, because it is easy for its back to become its front, and its oblique form helps in establishing a more ambiguous interpretation of the figure. It is combined with two other components, the green/black striped band and the red cube, both of which resist pseudoscopic interpretations*. Viewed through the Pseudoscope, the rhombus turns inside out; having the following effects:

1. It appears to rotate in the opposite direction,
2. Shadows cast behind appear in front of or level with the rhombus;
3. The striped band appears to rotate in the opposite direction to the rhombus,
4. he red cube floats in space, looks transparent, and rotates the wrong way,
5. Anyone who stands between the rhombus and the wall may appear to be inside the rhombus,
6. The red tubes separating the sheets of plexiglass show which end is pointing towards the observer because the tubes have internal shadow, nevertheless, the end's with the shadow will appear to be pointing away from the observer.
7. Perspective is reversed for the plexiglass sheets (their different edge finish helps to make this visible),
8. The light falling on the rhombus will appear to come from a source opposite its real source,
9. Reflections on the plexiglass will behave like shadows,
10. If the rhombus is rotated by hand clockwise, it will be exciting for an observer to see it rotating counter clockwise,
11. Concavities become convexities, convexities become concavities.

In spite of being dramatically contradictatory, some of these opposing movements occur so smoothly, that they can at first, and sometimes do, go unnoticed. This partly because it is unexpected, therefore it is worth indicating to the observer the direction against which the rhombus is really turning, and asking 'Is that the direction in which the figure is turning?'. You will frequently find the answer will be 'yes', so ask them to look at the figure without the Pseudoscope so they can see for themselves that it is actually going the other way.

The simplest way to see normally when you are looking through a pseudoscope is to shut one eye; having removed the pseudoscopic stimuli the direction of rotation of the rhombus will be correct, but most observers will notice that there is a slight delay in the switch from normal vision to pseudoscopic vision. Of course when the eye is opened again the pseudoscopic stimuli re-assert themselves, and by opening and closing one eye you will be able to make the rhombus appear to change direction at will.

The amount of delay - or hysteresis - will be longer for some people than others. The ability to make available alternative structural interpretations can be very interesting, particularly when applied to projections of higher dimensions, when it can be difficult to set aside conventional notions, and sustain a different referential frame. This does not of course apply to regular polytopes only, but to any structures which are responsive to spatial re-mapping. Experiments with several different kinds of subjects will be very rewarding and full of surprises.

If facilities are available, it would be worth considering the construction in transparent 1/8" inch (3mm) plexiglass of a hypercube in orthogonal projection. The hypercube is not only fascinating in itself, but is a beautiful pseudoscopic and hyperscopic object.

Shadows
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Having stated that the Pseudoscope turns space back to front, so that the background becomes the transparency through which the foreground is seen, the behavior of shadows is a convincing way of demonstrating it.

It is fairly easy to cast a strong sharp shadow using a 35mm projector(with no slide)as a light source because it can be focused. Through the Pseudoscope the shadow will appear to be level with or in front of the rhombus. It is as well at this stage to avoid a background with strong texture, as this might change the effect.

The Hypercube
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The Hypercube 12 tiles when joined together will make a simplified hypercube. Download a PDF with a stencil and instructions on how to make the hypercube depicted above. NB. Adobe Acrobat is needed to view this document and is available as a free download from Adobe

Click to open a window with a looping animation of the the 4D cube rotating 360° This animation may be "fused" and shows a stereoscopic rotating hypercube. A downloadable version is available in our shop which is fully scalable and gives the user full control over spin and rotation around different axies.. There is also a slow motion button . An n-Dimensional texture mapped cube with special lighting effects is shortly to follow.

12 tiles when joined together will make a simplified hypercube. Download a PDF with a stencil and instructions on how to make the hypercube depicted above.

NB. Adobe Acrobat is needed to view this document and is available as a free download from Adobe

Click to open a window with a looping animation of the the 4D cube rotating 360° This animation may be "fused" and shows a stereoscopic rotating hypercube. A downloadable version is available in our shop which is fully scalable and gives the user full control over spin and rotation around different axies.. There is also a slow motion button . An n-Dimensional texture mapped cube with special lighting effects is shortly to follow.

The Rolygon
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Two further models for use with the Pseudoscope could be constructed if facilities are available. Reference has already been made to the hypercube, but the model using two discs of plexiglass is simple to make and not only very dramatic for demonstrating effects, but may be considered as a model for a larger human-scale version.

The simplest way to make this figure is using a ½" inch (12mm) tube and drilling out the plexiglass discs to the same size hole, to fit the tube as a tight friction fit. It will be worth distinguishing the edges with continuous and broken lines as with the rhombus.

When this model is rolled across a plain floor, the Pseudoscope will make it look like a transparent bucket rolling on its edge beneath a transparent floor. If it is handled in the same way as the rhombus, hypercube etc., hands will seem transparent and their positions and movements will make no sense in relation to the model. If the model is given a slight twist, as in the diagram, it will move across the floor in roly-poly manner which looks even stranger. If it is made a reasonable size, say 12 inches (30cm) it could be used with the rhombus and red cube. It does not have to be a red cube - other colours may be used.

A human-scale model of this, about 6 ft (1.9m) high with a central axis for two seats for children to sit back to back would be very fascinating to see through the Pseudoscope, with slightly transparent children going in one direction and the model going in the other.

Any book of mathematical models will give details from which to construct simplex models from basic materials which will perform very well pseudoscopically, particularly if they are contrasted with things that do not work pseudoscopically, like striped bands or cubes, or if they are viewed being handled. They may also be suspended and used with the texture screen projections.

Hypertube
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The Hypertube dramatises the 'crossover paradox' as whole coloured sections suddenly switch between back and front. The Hypertube is also useful for your own experiments by suspending your own targets centrally and watching them rotate the 'wrong' way. Supplied with a hook and suspension cord and S hook.

Hypertubing may be purchased from our online shop.