Hexaflexagon Exploration
A worksheet exploring the geometry and construction of hexaflexagons, suitable for Grade 9 students.
Includes
Standards
Hexaflexagon Exploration
Name:
Date:
Score:
Follow the instructions for each section carefully. Show all your work where applicable.
Hexaflexagons are fascinating paper models that can be 'flexed' to reveal hidden faces. They are typically constructed from a strip of paper divided into equilateral triangles.
Consider a simple tri-hexaflexagon, which has three faces.
1. Which basic geometric shape is primarily used to construct a hexaflexagon?
Square
Circle
Equilateral Triangle
Rectangle
2. How many faces does a standard tri-hexaflexagon have?
Two
Three
Four
Six
3. The process of revealing hidden faces in a hexaflexagon is called .
4. A hexaflexagon is a type of puzzle.
5. Describe the key characteristic that makes a hexaflexagon unique compared to a regular paper polygon.
6. Imagine you are constructing a hexaflexagon. What geometric properties of an equilateral triangle are crucial for its successful construction and flexing?
7. All hexaflexagons have exactly six faces.
True
False
8. The 'pat' of a hexaflexagon refers to the sequence of faces revealed during flexing.
True
False
Below is a simplified representation of a strip of paper used to make a hexaflexagon. Each triangle represents a segment of the strip.
9. If each small equilateral triangle has a side length of 2 cm, what is the total length of the strip of paper shown above, assuming it's laid out flat before folding?
10. Research and explain the concept of a 'flexagon tree' and how it relates to the different states (faces) a hexaflexagon can exhibit. You can draw a simple diagram if it helps your explanation.