The reason for that change has nothing to do with adjectives or with the ending "-ísimo".
The writing change of your example is because of the /k/ + vowel sound that goes afterwards ("rico" is pronounced "/riko/"). The writing is different depending on the vowel following the /k/ sound. "e" and "i" are exceptions when they are following a consonant in some cases.
In my opinion (and this is how we learned it at school when we were kids) it is much better to think in sound groups that have exceptions in writing and learn them by heart, rather than thinking that "you have to change the writing to maintain the sound".
For the example you asked:
- /k/: ca, que, qui, co, cu
- Examples: Casa, quemar, quitar, comer, curar, are all pronounced the same (/kasa, kemar, kitar, komer, kurar/). In your case both are also pronounced the same (/riko->rikisimo/) but the orthography rule for /k/ + vowel makes the writing different: rico->riquísimo.
But this also happens with:
- /z/: za, ce, ci, zo, zu (as it sounds in Spanish from Spain, like the "th" in "think")
- Example: /zeniza/->ceniza
- /g/: ga, gue, gui, go, gu -> Gato, guerra, guiño, gorro, gubia.
- /g+u/: gua, güe, güi, guo -> Agua, desagüe, pingüino, antiguo. (Guu does not exist).
In some cases, two ways coexist, depending on the word:
- /j/: ja, ge/je, gi/ji, jo, ju
- Examples: Gema, jeroglífico. Girar, jirafa.
This is indeed extremely weird and confusing for children and for non-native speakers/writers. It has no logical explanation other than tradition, but that's how it is and it should be learned by heart.
Learn and practice those exceptions and you will automatize them quickly. There is no other way. This is what we did at school and believe me, it was for a reason. It's difficult, agreed, but there are not so many exceptions.
Think of the consonant+vowel sound combinations and say them aloud /ka, ke, ki, ko, ku/ while you write them down "ca, que, qui, co, cu". Say /ga, ge, gi, go, gu/ and write down "ga, gue, gui, go, gu". Etc.
You'll see how your Spanish improves really quickly.
Don't worry too much about the je/ge, ji/gi thing. Most Spanish make mistakes when writing words with /j/ + e,i sound combinations. What you really need to know though is that ge, gi always sound /je, ji/ (very important for reading aloud).
To understand to which extent this is weird and arbitrary, some oral languages that were written using Spanish orthography (e.g. Basque) recently got rid of all these exceptions/inconsistencies and simplified the writing.
Although this is quite recent (a few decades), the official and modern way of writing these consonant+vowel sound combinations in Basque is:
- /k/: ka, ke, ki, ko, ku
- /z/: za, ze, zi, zo, zu
- /g/: ga, ge, gi, go, gu
- /j/: ja, je, ji, jo, ju
As an interesting example, the traditional "Guipúzcoa" has become "Gipuzkoa" in modern Basque ortography.
