Symmetry

Question 1

Number of faces on a cube?

Answer 1

6

Question 2

Number of vertices on a cube?

Answer 2

8

Question 3

Number of faces on a tetrahedron?

Answer 3

4

Question 4

Number of faces on an octahedron?

Answer 4

8

Question 5

Number of vertices on a tetrahedron?

Answer 5

4

Question 6

“Procedure to Determine”

C_{<strong>2v</strong>}

Answer 6

“Procedure to Determine”

Not a special group

C_2​ (yes, principal axis)

No ⊥C₂

No σ_h

2σ_v

Question 7

Chiral Point Groups

Answer 7

C_n ,D_{<b>n </b>}T, O, and I groups only

Question 8

All chiral molecules are polar

True or False

Answer 8

False

(e.g. Molecules in the D_n point group are chiral but not polar.)

Question 9

Chiral Molecule

Answer 9

Molecules that lack an improper rotation axis

Question 10

“Procedure to Determine”

C Point Groups

Answer 10

“Procedure to Determine”

Not a special group

No n⊥C₂ to principal axis

Question 11

“Procedure to Determine”

D Point Groups

Answer 11

“Procedure to Determine”

Not a special Group

n⊥C₂ to principal axis

Question 12

“Procedure to Determine”

D_{<strong>5d</strong>}

Answer 12

“Procedure to Determine”

Not a special group

C_5​ (yes, principal axis)

5 ⊥C₂

No σ_h

5σ_d

Question 13

“Procedure to Determine”

C_{<strong>∞​V</strong>}

Answer 13

“Procedure to Determine”

Linear (Yes)

No ⊥C₂

Question 14

“Useful Matrices”

Answer 14

“Useful Matrices”

i

Question 15

“Point Groups”

Bent corresponding point group

Answer 15

C_2v

Question 16

“Point Groups”

SeeSaw corresponding point group

Answer 16

C_2v

Question 17

“Point Groups”

Square Planar corresponding point group

Answer 17

D_4h

Question 18

“Point Groups”

T-Shape corresponding point group

Answer 18

C_2v

Question 19

“Point Groups”

Trigonal Bipyramidal corresponding point group

Answer 19

D_3h

Question 20

“Point Groups”

Trigonal Planar corresponding point group

Answer 20

D_3h (SO₃)

C_2v (Acetone)

C_s (Methyl formate)

Question 21

“Point Groups”

Trigonal Pyramidal corresponding point group

Answer 21

C_3v

Question 22

σ_perp and σ_h are equivalent types of mirror planes?

True or False

Answer 22

False

Question 23

“Matrix Characters”

χ(S₁ )

Answer 23

1

Question 24

“Matrix Characters”

χ(σ )

Answer 24

1

Question 25

***"Matrix Characters"*** **χ(*i*)**

Answer 25

**-3**

Question 26

***"Matrix Characters"*** **χ(C₃)**

Answer 26

**0**

Question 27

***"Matrix Characters"*** **χ(C₂)**

Answer 27

**-1**

Question 28

**"*_Useful Matrices"_*** **χ (C₂)**

Answer 28

**"*_Useful Matrices"_*** **S₄(z)**

Question 29

**"*_Useful Matrices"_***

Answer 29

**"*_Useful Matrices"_*** **σ_h**

Question 30

**"*_Useful Matrices"_***

Answer 30

**"*_Useful Matrices"_*** **C_n(x)**

Question 31

**"*_Useful Matrices"_***

Answer 31

**"*_Useful Matrices"_*** **C_n(z)**

Question 32

**"*_Useful Matrices"_***

Answer 32

**"*_Useful Matrices"_*** **C₃(z)**

Question 33

**"*_Useful Matrices"_***

Answer 33

**"*_Useful Matrices"_*** **C₂(z)**

Question 34

**"*_Groups"_*** ***C Point Group***

Answer 34

![]()**"*_Groups"_*** **_No_ ⊥** **C₂ to principal axis**

Question 35

**"*_Groups"_*** ***D Point Group***

Answer 35

![]()**"*_Groups"_*** **Not a special group** **n ⊥** **C₂ to principal axis**

Question 36

## Footnote **Number of vertices in an octahedron**

Answer 36

![]() **6**

Question 37

**5 Platonic solids**

Answer 37

![]()

Question 38

***_"Operator"_*** **E**

Answer 38

***_"Operation"_*** **The _identity_ operator is the "do nothing" operator. All points remain at their original position.**

Question 39

***_"Operator"_*** **i**

Answer 39

***_"Operation"_*** **Projects each atom through the center of symmetry to its negative xyz position.**

Question 40

***_"Operator"_*** **σ_h**

Answer 40

***_"Operation"_*** **A mirror plane perpendicular to the principal axis.**

Question 41

***_"Operator"_*** **S_n**

Answer 41

***_"Operation"_*** **A combination of Cn followed by σ_perp yields an improper rotation**

Question 42

***_"Operator"_*** **C_n**

Answer 42

***_"Operation"_*** **A n-fold [360º/n] clockwise rotation about an axis**

Question 43

**Operations with** **axial symmetry elements**

Answer 43

## Footnote **C_n and S_n**

Question 44

**operations using a point symmetry element**

Answer 44

## Footnote **E and i**