Emails between me and Andrew Clarke:
LIVIO: I'll open a section about examinoes...
ANDREW: I am interested in what you mean by 'examinoes'
LIVIO: Dear Andrew, it's a mistake, simply a mistake! My English is not good.The ancient Greeks said EXA-GONOS (Epsilon, Xi, Alfa...) for hexagon. The ancient Romans, SEX-ANGULUM, but I think SEX- has an other meaning in English! :-) When & why the "H" is born?
ANDREW: In classical Greek there was an 'h' sound before some words starting in a vowel but they had no symbol for it. The H comes from the Romans who used a symbol over the first vowel of a Greek word to show whether or not it had an 'h' sound. (The two symbols used were halves of the Greek capital eta hence the H). This was to make it easier for the Romans to learn Greek.
LIVIO: I think that 'Domino' is a false compund noun like 'Bikini'. Probably the 'Domino' game has introduced in Europe by a Domino Abbe (from Dominus, God). But the Domino piece is formed by two squares and we thought that the meaning was DUO-MINO. With Greek words TETRA, PENTA, EXA, in Italian we formed TETRA-MINO, PENTA-MINO, ESA-MINO. Why do you say "tetrOmino,pentOmino, hexOmino" ?
ANDREW: I think this comes from the fact that DOMINO is taken to be shortening of DI-OMINO and the final vowel of the prefix is omitted. It is probable that the Italian PENTAMINO etc. may be better but I suppose we must blame Golomb!
In the night I haven't forgotten the suffix SEX of SEXangulum. I read an old book about puzzles, made by little squares of cardboard, with male and female dovetail . I said: "These are SEXOMINOES!". The book only was talking about old puzzles of cardboard that everybody knows. But I never seen a mathematical discussion. Probably I am wrong. Let me try to talk about:
I think there is only one sexomino with angel-sex and only two hetero-sex, the male and the female:
The bi-sex are seven (one side). I am lucky to find four angles:
The tri-sex are eight (one side), like a binary number of three figures:
And there are six tetra-sex:
This is a miracle. There are 24 pieces to make a rectangle of 6x4. There are four angles. There are 32 females for 32 males. There are rectilinear edges in good number. There is a solution at least:
This is one. You could find other solutions. (How many solutions are there?) I go and see if I could talk about sex-cubes...
Below the title there is the same thing, but in minimal art.
We could do the same thing using equilateral triangles. Here we are less lucky. However, these are the possible eleven sex-triangles (one side): 1 neutral, 1 male, 1 female, 4 bi-sex e 4 tri-sex:
By nine sex-triangles we could do a good triangle. By the last two we can tile the plane:
"Sexehexes" is an other chapter.