Pater dicit formam huius conchae pulchriorem esse quam illius.

The key pattern is indirect statement, also called the accusative-and-infinitive construction.

After a verb like dicit (says), Latin often does not use a clause with that the way English does. Instead, it uses:

• an accusative noun as the subject of the reported statement
• an infinitive as the verb of that statement

So here:

• Pater dicit = Father says
• formam ... esse = the shape ... to be

A direct version would be:

• Forma huius conchae pulchrior est quam illius.
• The shape of this shell is more beautiful than that of that one.

When that statement is reported after dicit, forma becomes formam, and est becomes esse.

Because formam is the subject of the infinitive esse inside an indirect statement.

In English, we say:

• Father says that the shape is more beautiful.

In Latin, that becomes:

• Father says the shape to be more beautiful.

So formam is accusative because in this construction, the subject of the reported statement goes into the accusative.

If it were a normal standalone sentence, it would be nominative:

• forma ... pulchrior est

But after dicit, it becomes:

• formam ... pulchriorem esse

For the same reason: this is an indirect statement.

In a direct statement, Latin would use a finite verb:

• Forma huius conchae pulchrior est.

But after dicit, Latin usually changes the verb of the reported statement into an infinitive:

• formam huius conchae pulchriorem esse

So:

• est = is
• esse = to be

Latin prefers accusative + infinitive after verbs of saying, thinking, knowing, hearing, and similar verbs.

Huius conchae is genitive singular, meaning of this shell.

Breaking it down:

• huius = genitive singular of hic, haec, hoc = this
• conchae = genitive singular of concha = shell

Together they describe whose shape is being discussed:

• forma huius conchae = the shape of this shell

So conchae depends on formam, showing possession or relationship.

Because the sentence needs the genitive singular, not the nominative.

You are not saying:

• this shell
• that shell

You are saying:

• of this shell
• of that one / of that shell

So Latin uses:

• huius = of this
• illius = of that

These are the genitive singular forms of the demonstratives:

• hic, haec, hoc → huius
• ille, illa, illud → illius

A useful thing to remember is that many pronouns and pronominal adjectives have genitive singular in -ius.

Because it is:

• the comparative form of pulcher = beautiful
• and it agrees with formam

Since formam is:

• feminine
• singular
• accusative

the adjective must match it:

• pulchriorem = feminine/masculine accusative singular comparative

So:

• forma pulchrior = the shape is more beautiful
• formam pulchriorem esse = the shape to be more beautiful

Even though the comparative form often looks similar across masculine and feminine, here the important point is that it matches formam in case and number.

It means than that one’s or than that of that one.

Here illius means of that one / of that shell. Latin is leaving out a repeated word because it is obvious from context.

The comparison is really between two shapes:

• the shape of this shell
• the shape of that one

So the full sense is something like:

• formam huius conchae pulchriorem esse quam formam illius
• the shape of this shell to be more beautiful than the shape of that one

Latin often omits repeated words when they are easy to understand.

No. Quam itself does not force illius to be genitive.

Illius is genitive because it means of that one. The genitive idea belongs to illius, not to quam.

So:

• quam = than
• illius = of that one

The genitive is there because the sentence is really comparing one shape with another shape belonging to that one.

Yes. Latin word order is much more flexible than English word order.

This sentence is arranged in a very natural Latin way:

• Pater dicit first gives the main statement
• then comes the indirect statement
• esse comes near the end
• quam illius finishes the comparison

Latin uses word order more for emphasis and style than for basic grammar, because the endings already show the grammatical roles.

So the order matters less than the forms:

• pater is nominative
• formam is accusative
• huius conchae is genitive
• pulchriorem agrees with formam
• esse is the infinitive

Those endings tell you how the sentence works.