Play the card game "Set"

Question

"Set" is a card game played with a deck of 81 cards, twelve of which are pictured below:

Each card has four attributes, each of which may assume three values:

• Number: the number of symbols, either 1, 2, or 3
• Shape: the shape of the symbol, either squiggle, diamond or oval
• Colour: either purple, red or green
• Shading: symbols may be solid, half-shaded or empty.

Each of the 3^4 = 81 possible combinations of these attributes appears on exactly one card in the deck.

Cards can be specified via a four-character string where one character specifies each attribute: "1", "2", or "3" for number; "s", "d", or "o" for squiggle, diamond or oval; "p", "r" or "g" for colour, and "s", "h" or "e" for solid, half or empty shading.

In this notation, the top row above is "3sph", "2dre" and "1ops".

Given a collection of twelve such cards, the object of the game is to be the first player to identify a subset containing three cards such that, for each of their four attributes, either:

• each card has a different value for that attribute, or
• all cards have the same value for that attribute.

To quote Wikipedia: 'The rules of Set are summarized by: If you can sort a group of three cards into "two of ____ and one of ____", then it is not a set.'

In the image above, an example of a valid set would be the first, second and seventh cards ("3sph", "2dre" and "1ogs"). There are five other valid sets in this image.

Challenge

Take as input a list of twelve cards. They may be specified in the four-character notation described above, or you may invent your own.

Output a list of all valid three-card sets therein.