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The Fourth Dimension Trivia Quiz

Mathematicians can visualise space of four, five, or even an infinite number of dimensions. How much do you know?

A multiple-choice quiz by BTD6_maker. Estimated time: 4 mins.

Author
BTD6_maker

Time
4 mins

Type
Multiple Choice

Quiz #
360,230

Updated
Dec 03 21

# Qns
10

Difficulty
Difficult

Avg Score
5 / 10

Plays
729

Last 3 plays: Guest 172 (4/10), Guest 51 (3/10), Guest 61 (6/10).

One at a Time - Single Page - Timed Game

Question 1 of 10

1. What is the name of a four-dimensional cube? Hint

3-sphere

4D Cube

Tesseract

Cubachoron

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Question 2 of 10

2. How many vertices does a tesseract have? Hint

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Question 3 of 10

3. There are 5 Platonic solids or, as mathematicians like to call it, regular 3-polytopes. How many regular 4-polytopes exist? Hint

An infinite number

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Question 4 of 10

4. In 5 or more dimensions, there is always the same number of regular polytopes. What number is this? Hint

An infinite number

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Question 5 of 10

5. What is the difference between 4 space dimensions and 3 space 1 time? Hint

The distance between two points is always negative in 4-space.

The distance formula contains a -t^2 term in space-time.

Both of these.

None of these.

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Question 6 of 10

6. A tesseract has 8 "cells" (3D shapes on it, just like a 3D solid has faces).

True

False

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Question 7 of 10

7. Circles can be linked in 4-space.

True

False

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Question 8 of 10

8. How many analogues of the cylinder exist in 4-space? Hint

An infinite number

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Question 9 of 10

9. A tesseract with sides 1/2 has diagonals of less than 1.

True

False

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Question 10 of 10

10. How many edges, respectively, do a cube in 3 dimensions and a tesseract in 4 dimensions have? Hint

20 and 40

12 and 36

12 and 32

Both have 24

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Most Recent Scores

Dec 20 2024 : Guest 172: 4/10
Dec 18 2024 : Guest 51: 3/10
Dec 15 2024 : Guest 61: 6/10
Nov 30 2024 : Guest 188: 5/10
Nov 14 2024 : Guest 1: 5/10

Score Distribution

Quiz Answer Key and Fun Facts

1. What is the name of a four-dimensional cube?

Answer: Tesseract

The 3-sphere is a sphere in 4 dimensions. It is a 3D shape, just as a sphere (sphere refers to the surface only) in 3 dimensions is a 2D shape. Cubachoron is a made up word.

2. How many vertices does a tesseract have?

Answer: 16

It is easy to see that a line segment has 2, a square has 4, and a cube has 8. In this case the progression works so it follows that a tesseract has 16.

3. There are 5 Platonic solids or, as mathematicians like to call it, regular 3-polytopes. How many regular 4-polytopes exist?

Answer: 6

Three of these correspond to the tetrahedron, the cube, and the octahedron. These three only exist in three or more dimensions (apart from the tetrahedron/triangle) since the analogue of a cube is a square, which also corresponds to the octahedron.

4. In 5 or more dimensions, there is always the same number of regular polytopes. What number is this?

Answer: 3

As before, these correspond to the tetrahedron, the cube, and the octahedron.

5. What is the difference between 4 space dimensions and 3 space 1 time?

Answer: The distance formula contains a -t^2 term in space-time.

However, relativity assigns a negative distance to some points. These are all the points it is possible to travel to or come from relative to the starting point.

6. A tesseract has 8 "cells" (3D shapes on it, just like a 3D solid has faces).

Answer: True

A line has 2 end points, a square has 4 edges, a cube has 6 faces, so a tesseract has 8 cells. This time it is a linear progression.

7. Circles can be linked in 4-space.

Answer: False

However, spheres can be linked in 5-space and 3-spheres in 7-space.

8. How many analogues of the cylinder exist in 4-space?

Answer: 3

These are the cubinder, the duocylinder, and the spherinder. Just as a cylinder is a circle moved in a line, a spherinder is a sphere moved in a line, a duocylinder is a circle moved in a circle, and a cubinder is a square moved in a circle.

9. A tesseract with sides 1/2 has diagonals of less than 1.

Answer: False

Using the distance formula, the diagonal is exactly 1.

10. How many edges, respectively, do a cube in 3 dimensions and a tesseract in 4 dimensions have?

Answer: 12 and 32

In five dimensions a cube has 80 edges and 192 in six dimensions. The general formula in n dimensions is n(2^(n-1))

Source: Author BTD6_maker

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
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