The question is: how many triangles are there in a 'Mystic Rose' shape like this one (right) - with six interconnected points.
I reckon there are 110.
I got this by splitting it up into different types of triangle, like this:
|One triangle||18||6 on the edge (isosceles), 12 at the corners (right-angled)|
|2T||18||12 x edge + corner (right-angled); 6 x double-corner (equilateral)|
|3T||12||Right-angled triangle along edge|
|4T||6||All the way along the edge (isosceles)|
|1 triangle, one quad||12||Right-angled triangle involving vertex and centre|
|3T 1Q||6||Equilateral triangle into middle|
|2T 2Q||6||Centre and two non-adjacent corners (isosceles)|
|2T 3Q||6||Isosceles triangle with two opposite corners|
|3T 3Q||12||Right-angled triangle with non-adj corners|
|5T 3Q||12||Right-angled triangle with three vertices|
|6T 6Q||2||"Star of David" equilateral triangles|
I keep adding it up differently, but I'm pretty happy that it's 110 now.
Note that all of the triangles involve at least one vertex. Apart from the "star of David" triangles in the middle, the isosceles/equilateral triangles come in groups of six and the right-angled (scalene) triangles come in groups of 12.