Hexaflexagon Exploration
Explore the geometry and properties of hexaflexagons with this Grade 11 math worksheet.
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Hexaflexagon Exploration
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Read each question carefully and provide your best answer. Show your work where applicable.
A hexaflexagon is a flat model, usually constructed from paper, that can be folded in such a way as to expose new faces. The simplest type is the trihexaflexagon, which has three faces.
Consider a strip of paper made of 10 equilateral triangles, joined along their edges. This strip can be folded to form a trihexaflexagon. The diagram below shows the basic structure of such a strip.
1. What geometric shape forms the fundamental unit of a hexaflexagon?
Square
Pentagon
Equilateral Triangle
Hexagon
2. A trihexaflexagon typically has how many faces that can be flexed into view?
2
3
4
6
3. The process of folding a hexaflexagon to reveal a new face is called .
4. A hexaflexagon is a type of polygon.
5. Describe the construction process of a simple trihexaflexagon, starting from a strip of paper with equilateral triangles. What are the key steps in folding it?
6. All hexaflexagons have exactly six faces.
True
False
7. The number of faces on a hexaflexagon is determined by the number of triangles in the initial strip.
True
False
8. Explain how the concept of 'flexing' a hexaflexagon relates to topological transformations. What properties remain invariant during a flex?