1.
How many faces of a tritetraflexagon is visible at a time?
Correct Answer
A. 3
Explanation
A tritetraflexagon is a geometric shape that can be folded and flexed to reveal different faces. It is made up of four equilateral triangles. When the tritetraflexagon is folded and flexed, three faces are visible at a time, while one face remains hidden. Therefore, the correct answer is 3.
2.
How many triangles make up a hexahexaflexagon?
Correct Answer
B. 19
Explanation
A hexahexaflexagon is a six-sided polygon that can be folded into different configurations. Each side of the hexahexaflexagon can be divided into three triangles. Since there are six sides, there are a total of 6 x 3 = 18 triangles. Additionally, there is an extra triangle formed in the center when the hexahexaflexagon is folded. Therefore, the total number of triangles in a hexahexaflexagon is 18 + 1 = 19.
3.
How can you expose all the faces of a flexagon?
Correct Answer
A. Using Tuckerman reverse
Explanation
One can expose all the faces of a flexagon by using Tuckerman reverse. Tuckerman reverse is a technique used to fold and unfold flexagons in a specific way that allows all the faces to be visible. This technique involves carefully manipulating the flexagon by folding and unfolding it in a specific sequence, which ultimately reveals all the hidden faces.
4.
What type of triangles can you use to create a hexaflexagon?
Correct Answer
C. Equilateral
Explanation
An equilateral triangle is a type of triangle that has all three sides of equal length. When you create a hexaflexagon, you fold a strip of paper into a hexagon shape, and each side of the hexagon is made up of an equilateral triangle. Therefore, to create a hexaflexagon, you need to use equilateral triangles.
5.
How can you create a higher octaflexagon?
Correct Answer
A. Converting the triangle to right angle
Explanation
To create a higher octaflexagon, you need to convert the triangle to a right angle. This means changing the shape of the triangle so that it has one 90-degree angle. This alteration is necessary because an octaflexagon is a paper model with eight faces, and each face is a different triangle. By converting the triangle to a right angle, you ensure that the resulting octaflexagon will have the correct shape and number of faces.
6.
Which type of flexagon was first discovered?
Correct Answer
C. Tritetraaflexagon
Explanation
The Tritetraflexagon was the first type of flexagon to be discovered. Flexagons are paper models that can be folded and flexed to reveal different faces. The Tritetraflexagon is made from a strip of paper folded into a triangle shape, with three different faces that can be revealed by flexing the paper. It was first discovered by Arthur Stone in the 1930s.
7.
What are the angles in a pentaflexagon?
Correct Answer
B. 72-54-54
Explanation
A pentaflexagon is a polygon with five sides that can be folded in different ways to reveal different angles. The given answer, 72-54-54, suggests that the angles in a pentaflexagon are 72 degrees, 54 degrees, and 54 degrees. These angles may correspond to the internal angles of the pentaflexagon when it is folded or manipulated in a specific way.
8.
How can one create a dodecaflexagon from a pentaflexagon?
Correct Answer
B. By dividing its triangles
Explanation
To create a dodecaflexagon from a pentaflexagon, one needs to divide its triangles. This means that the original pentaflexagon's triangles are divided into smaller sections, resulting in a dodecaflexagon with twelve sides. This process involves cutting along certain lines and rearranging the sections to form the new shape.
9.
What do you call a flexagon that cannot be flexed?
Correct Answer
B. Non-planar
Explanation
A flexagon is a flat geometric shape that can be folded and flexed to reveal different faces or patterns. If a flexagon cannot be flexed, it means that it cannot be folded or manipulated to show different sides or patterns. In other words, it remains in a fixed, unchanging position. The term "non-planar" refers to an object or shape that does not lie completely flat on a single plane. Therefore, a flexagon that cannot be flexed is considered non-planar because it cannot be folded or manipulated to lie flat on a single plane.
10.
Which of these types of flexagon cannot be flexed?
Correct Answer
A. Heptaflexagon
Explanation
A heptaflexagon cannot be flexed because it has an odd number of sides. Flexagons are made by folding a strip of paper or card in a specific way so that different faces can be revealed by flexing or bending the shape. However, with an odd number of sides, it is not possible to fold the strip in a way that allows for flexing and revealing different faces.