COC6 fixates mostly on d6's and d10's - the d10 pair being used a lot.
d6's are used in character generation, and often for damage.
There are plenty of d8 SAN loss entries. Steal Life (p. 243) is a 1d20 SAN loss to cast.
Commercially, d3's as such are rare. Most dice sets don't include them. D2's are even rarer - just use the d6 to simulate both.
Only the d12 isn't actually used in COC6 in some way, and even then, it's the traditional die for "What time is it?" rolls.
Basic Role Play Engine Games in General
In General, the BRP line has used d6's for attributes, d100 for rolling skills, and d20 for hit locations.
Damages have traditionally been d3, d4, d6, d8, or d10.
Runequest 3rd edition shipped with 4d6, 1d8, and 2d20 - you used the d20's for rolling percentiles and as both d10's and d20's.
ElfQuest avoided even the d8's.
To find d12's in use in BRP, one must go back to RQ 1E - 2E still includes mention of them, but the errata notes that they were dropped from the mechanics. (This was 1980...)
A Bit of Dice History
Initially, the gaming industry used almost exclusively d6's.
In the 60's, d20's were becoming available for wargaming use, easily allowing generation of 1-4, 1-5, 1-10, and 1-20 results. These were sold as 10-sided dice, however - they were usually numbered 0-9, and read 1-10.
In the early 1970's, the Platonic Solids were added by Gygax to the dice repertoire. This gave d4, d6, d8, d12, and d20 in physical dice, but the 20's were still typically 0-9 twice. A few years later, still before 1979, the 1-20 d20 was introduced.
The modern d10, the pentagonal trapezohedron, was introduced in 1980. by 1990, some sets had the d10x10 (marked 00, 10, 20, 30, 40, 50, 60, 70, 80, 90), while others simply included a different colored second d10.
"Standard sets" have always focused on D&D play - D&D drove the hobby until the 1990's, and is still a major force. Pathfinder, a D&D 3E derivative, is has taken over the industry leader position, but still retains the majority of D&D-isms.
There are several types of standard set:
- Yachtze Set: 5d6. This is the standard for cheap dice, and has been since the early 20th century.
- Backgammon set: 4d6. The standard for backgammon in the 20th century. Often sold as two contrasting pairs of 2d6.
- TSR's original set: 1d4, 1d6, 1d8, 1d12, 1d20
- TSR's D&D Set: 1d4, 1d6, 1d8, 1d10, 1d12, 1d20. Percentiles were rolled using 1d20 and 1d10, or using d10's from two sets.
- The Player's D&D set: 1d4, 3d6, 1d8, 2d10, 1d12, 1d20. the second d10 was usually off color. the 3d6 were a matched set.
- 4d6 - some versions added a 4th d6.
- d10x10 - modern versions replace the off-color d10 with a d10x10 matched.
- Modern short set: 1d4, 1d6, 1d8, 1d10, 1d10x10, 1d12, 1d20
- Modern long set: 1d4, 4d6, 1d8, 1d10, 1d10x10, 1d12, 1d20
- D10's set: 10d10. Used for a number of games, it was introduced as a set in the early 1990's, primarily for use with White Wolf's games.
- "Cubes" of d6 - typically 27d6, 36d6 or 45d6. Sold for wargamers, but useful in some RPG's (Shadowrun and T&T).
There has never been a commercial BRP focused set that I've seen - the dice in RuneQuest were bought by Chaosium in bulk, and included in the box, but generally, players bought individual loose dice.