Deck 17: Polyhedra

Question 1

Every n-gonal pyramid has n + 1 faces.

Answer 1

True

Question 2

Every n-gonal pyramid has n + 1 vertices.

Answer 2

True

Question 3

It is impossible for the number of edges, the number of faces, and the number of vertices to all be odd numbers, no matter what polyhedron you have.

Answer 3

True

Question 4

Complete the following sentences.

A) A prism with 16 vertices is a(n) _____ prism.
B) A hexagonal prism has _____ edges, _____ vertices, and _____ faces.
C) A pyramid with 60 edges has _____ vertices and _____ faces.
D) A pentagonal prism has _____ edges, _____ vertices, and _____ faces.

Question 5

Complete the following sentences.

A) A hexagonal prism has _____ lateral edges, _____ edges in all, and _____ vertices.
B) A rectangular pyramid has _____ edges, _____ vertices, and _____ faces.
C) A prism with 9 faces has _____ vertices and _____ edges.
D) A pyramid with 32 edges has _____ faces and _____ vertices.
E) A polyhedron with 6 vertices and 8 faces has _____ edges.

Question 6

I am a polyhedron with a total of nine faces. My lateral faces are isosceles triangles.
What is my full name?

Question 7

How many faces, edges, and vertices does a 100-gonal prism have? Justify two of the three counts without using a formula.
Number of faces _____
Justification:
Number of edges _____
Justification:
Number of vertices _____
Justification:

Question 8

Is it possible for the number of edges, the number of faces, and the number of vertices of a polyhedron to all be even? If so, give an example. If not, explain why not.

Question 9

Complete the following sentences.

A) A pyramid with 16 edges has _____ faces and _____ vertices.
B) A polyhedron with 14 faces and 21 edges has _____ vertices.
C) A polyhedron with 20 faces and 12 vertices has _____ edges.
D) A polyhedron with 11 vertices and 20 edges has _____ faces.

Question 10

A hexagonal pyramid has how many edges?

A) 5
B) 6
C) 10
D) 12
E) None of the answers is correct.

Question 11

A polyhedron with 14 vertices and 6 faces will have how many edges?

A) 5
B) 6
C) 8
D) 18
E) More information is needed to answer the question.

Question 12

An n-gonal pyramid has how many total edges?

A) n
B) n + 1
C) 2n
D) 3n

Question 13

Name the polyhedron that the net below gives.

A) heptagon
B) rectangular prism
C) rectangular pyramid
D) triangular prism
E) None of the answers is correct.

Question 14

I am a polyhedron with a total of nine faces. My eight lateral faces are isosceles triangles, all alike. My BEST name is:

A) nine-gon.
B) octagonal pyramid.
C) nine-gonal pyramid.
D) octagonal prism.
E) regular octagonal pyramid.
F)Triangular pyramid.

Question 15

Complete the following sentences.

A) A pentagonal prism has _____ vertices.
B) A 70-gonal pyramid has _____ edges.
C) An n-gonal prism has _____ lateral edges.
D) A polyhedron that has 18 faces and 32 vertices has _____ edges.
E) The lateral faces of pyramids are _____.

Question 16

Complete the following sentences.

A) An octagonal prism has _____ edges (in all) and _____ vertices.
B) An n-gonal pyramid has _____ lateral edges and _____ faces.
C) A prism that has 12 faces in all has _____ vertices.
D) A polyhedron with 250 edges and 102 vertices has _____ faces.

Question 17

State Euler's formula for polyhedra.

Question 18

What is the sum of the number of edges and the number of vertices of an octagonal pyramid?

A) 25
B) 22
C) 9
D) 23
E) None of the answers is correct.

Question 19

Which statement is safe to say about every square pyramid?
I. Every lateral edge has the same length.
II. all of the angles on each face are equal.
III. Every base edge has the same length.

A) I only
B) II only
C) III only
D) I and III only
E) some choice among I, II, and III that is not given here

Question 20

What is the name of the shape below?

A) polyhedron
B) eight-gon
C) hexagonal prism
D) octahedron
E) L-pyramid

Question 21

A 100-gonal prism has _____ faces, _____ edges, and _____ vertices.

Question 22

A rectangular pyramid has _____ edges, _____ faces, and _____ vertices.

Question 23

Which statement is TRUE for every square prism?
I. Every angle in every face is a right triangle.
II. Every lateral edge has the same length.
III. All the edges have the same length.

A) I and II only
B) I and III only
C) II and III only
D) I, II, and III
E) None of the answers is correct.

Question 24

What is the sum of the number of faces and the number of vertices of an n-gonal prism?

A) 2n
B) n + 2
C) 3n
D) 3n + 2
E) None of the answers is correct.

Question 25

Which statement is TRUE about every right rectangular prism (rectangular solid)?
I. All the edges have the same length.
II. All the angles on each face have the same size.
III. Each edge is perpendicular to the edges it meets.

A) I only
B) II only
C) III only
D) II and III only
E) None of the answers is correct.

Question 26

What is the BEST technical name for a filing cabinet?

A) box
B) square box
C) prism
D) right prism
E) square prism

Question 27

Which figures are nets for a cube and which are not?

Question 28

Sketch a net for a right rectangular prism. (If your sketch is "off" in important ways, write your intentions as well.)

Question 29

Give the BEST name for the three-dimensional shapes represented by the following pictures. Note: Angles that look like right angles are right angles in the three-dimensional shape.

Question 30

Give the BEST name for the represented shapes.

Question 31

Draw, as carefully as possible, the following figures.

A) a right pentagonal prism
B) a triangular pyramid

Question 32

Draw a net for a cube in two different ways.

Question 33

On isometric dot paper, sketch a diagram of a shape that has the views shown in the figure below.

Question 34

How many nets form a square pyramid? Sketch.

Question 35

How many faces CANNOT be seen in the drawing of a hexagonal pyramid?

Question 36

Sketch a pentagonal pyramid. Be sure to include the hidden edges. Is your pyramid right or oblique?

Question 37

Use the following net to make a three-dimensional drawing of the unknown shape. Use hidden lines where necessary.

Question 38

Sketch the listed views for the three-dimensional drawing shown below.

Question 39

(Note to instructor: Preparation before the test is necessary.)
For Model X on your table:
1) Draw a net. (You are not allowed to take the model on your table apart, but feel free to pick it up.)
2) Draw a picture of the model.
3) State the correct mathematical name for Model X,
For Model Y on your table, draw a net.

Question 40

A) How many vertices does a 50-gonal pyramid have? Explain how you figured it out.
B) How many edges does a 50-gonal pyramid have? Explain how you figured it out.

Question 41

Which shapes are congruent? If none are congruent, explain how you know.

Question 42

A) On isometric grid paper, sketch a three-dimensional shape with the views shown below. Interpret "front" to be "front left" and "right" to be "front right."
B) On isometric grid paper, sketch a shape congruent to the one above but from a different viewpoint.

Question 43

A) There are _____ types of regular polyhedra.
B) Name the types.

Question 44

Explain why a cube is a regular polyhedron.

Question 45

What is a regular polyhedron?

Question 46

Each edge of a regular polyhedron has the same length.

Question 47

One of the types of regular polyhedra was only discovered in 1914.

Question 48

Every cube is a regular polyhedron.

Question 49

Every regular polyhedron is a cube.

Question 50

Close approximations to regular polyhedra do occur in nature.

Question 51

Name two platonic solids and the regular polygon of which each is made up. Then list the numbers of vertices, edges, and faces for each.
Name of solid $\quad$ Polygon used for faces $\quad$ #Vertices $\quad$ #Edges $\quad$ #Faces