Lets say you have 100 aliens and they have 30 traits of which there are different alleles of those traits.

Face Shape:
Round: 71
AA: 21%
Aa: 50%
Square: 29

Chin Size:
Prominent: 79
BB: 53%
Bb: 26%
Not Prominent: 21

Chin shape:
Round: 74
CC: 23%
Cc: 51%
Square: 26

Cleft chin:
Present: 77
DD: 48%
Dd: 29%
Absent: 23

Skin color:
Lightest(0 dominant): 2
Light(1 dominant): 14
Medium light(2 dominant): 21
Medium(3 dominant): 32
Medium dark(4 dominant): 23
Dark(5 dominant): 6
Darkest(6 dominant): 2

Hair color:
Light blonde(all recessive): 2
Medium light blonde(1 dominant): 8
Blonde(2 dominant): 10
Dark blonde(3 dominant): 22
Light brown(4 dominant): 25
Brown(5 dominant): 22
Dark brown(6 dominant): 9
Darkest brown(7 dominant): 2
Black(8 dominant): 0

Red tints:
Dark red tints(L1L1): 28
No red tints(L2L2): 26
Light red tints(L1L2): 46

Hair type:
Curly(M1M1): 22
Straight(M2M2): 25
Wavy(M1M2): 53

Widow's peak:
Present: 81
OO: 22%
Oo: 59%
Absent: 19

Eye color:
Black(PPQQ): 7
Dark brown(PPQq): 15
Brown(PpQq): 30
Brownish green(PpQQ): 15
Purple(PPqq): 7
Gray(more like a blue-gray)(Ppqq): 9
Green(ppQQ): 1
Dark blue(ppQq): 11
Light blue(ppqq): 5

Eye distance:
Close(R1R1): 28
Far(R1R2): 21
Average(R2R2): 51

Eye size:
Large(S1S1): 28
Medium(S1S2): 52
Small(S2S2): 20

Eye shape:
Almond: 76
TT: 22%
Tt: 54%
Round: 24

Eye slant:
Horizontal: 76
UU: 24%
Uu: 52%
Slanted: 24

Eyelashes:
Long: 73
VV: 27%
Vv: 46%
Short: 27

Eyebrow color:
Hair color(W1W2): 48
Darker(W1W1): 23
Lighter(W2W2): 29

Eyebrow thickness
Bushy: 71
ZZ: 29%
Zz: 42%
Fine: 29

Eyebrow length:
Apart: 93
Connected: 7
A2A2: 30%
A2a2: 45%
a2a2: 25%
Now how can there be 7 connected and 93 apart yet there be 30 homozygous dominant, 45 heterozygous, and 25 homozygous recessive?

Mouth size:
Long(B1B1): 26
Medium(B1B2): 46
Short(B2B2): 28

Lip thickness:
Thick: 68
C2C2: 27%
C2c2: 41%
Thin: 32

Dimples:
Present: 70
D2D2: 23%
D2d2: 47%
Absent: 30

Nose size:
Large(E1E1): 30
Medium(E1E2): 42
Small(E2E2): 28

Nose shape:
Rounded: 74
FF: 23%
Ff: 51%
Pointed: 26

Nostril shape:
Rounded: 75
GG: 29
Gg: 46
Pointed: 25

Earlobes:
Free: 69
HH: 22
Hh: 47
Attached: 31

Darwin's Ear Points:
Present: 76
II: 28
Ii: 48
Absent: 24

Ear pits:
Present: 63
JJ: 26
Jj: 37
Absent: 37

Hairy ears:
Hairy: 74
KK: 21
Kk: 53
No hair: 26

Freckles on Cheeks:
Present: 77
LL: 26
Ll: 51
Absent: 23

Freckles on Forehead:
Present: 74
MM: 25
Mm: 49
Absent: 26

Now that I have put in the numbers for each phenotype(apperance) under their respective traits and the genotype(actual gene combination) and I know how to do Punnet squares like this:
B b
B BB Bb
b Bb bb
and for 2 or more traits(which also applies to polygenic traits) but how am I supposed to do it for 30 traits of which some are polygenic(more than 1 gene? 30^2 = 900. There are lots of combinations of traits to calculate probability that an offspring will have some combination of traits. Also even if testing all combinations was possible it is much easier to understand with punnet squares and the alleles and half of each genotype being male and half of it being female.