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Quiz about The Fourth Dimension
Quiz about The Fourth Dimension

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.
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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
710
Last 3 plays: Guest 120 (2/10), Guest 109 (5/10), 14056 (4/10).
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Question 1 of 10
1. What is the name of a four-dimensional cube? Hint


Question 2 of 10
2. How many vertices does a tesseract have? Hint


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


Question 4 of 10
4. In 5 or more dimensions, there is always the same number of regular polytopes. What number is this? Hint


Question 5 of 10
5. What is the difference between 4 space dimensions and 3 space 1 time? Hint


Question 6 of 10
6. A tesseract has 8 "cells" (3D shapes on it, just like a 3D solid has faces).


Question 7 of 10
7. Circles can be linked in 4-space.


Question 8 of 10
8. How many analogues of the cylinder exist in 4-space? Hint


Question 9 of 10
9. A tesseract with sides 1/2 has diagonals of less than 1.


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



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Most Recent Scores
Mar 20 2024 : Guest 120: 2/10
Feb 19 2024 : Guest 109: 5/10
Feb 05 2024 : 14056: 4/10
Feb 05 2024 : Guest 203: 6/10
Jan 31 2024 : Guest 75: 2/10

Score Distribution

quiz
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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