Dodecahedron by vertices coordinates

What is the simplest way to build a dodecahedron from the coordinates of the vertices with right rotation?
Without using all the coordinates of the vertices, preferably with a minimum number of vertices. Example in the picture.

It’s not three.js specific question, but about spatial geometry.
Having those five verts, that are co-planar, how do you know the direction of “growth” of the dodecahedron? Above or under the plane the points form?

Thanks for the answer, it is not important to take these 5 points, you can take any points: the main thing is not to take all coordinates of the vertices and get the right position and rotation. For example y can take 4 vertices in middle.

I didn’t get, if you get three random vertices, how will you determine dodecahedron’s center? :thinking:

Its not random points, I will strictly set the indices of these points and save to xml and then from xml i need recreate dodecahedron

const point0Coordinate = new THREE.Vector3().fromBufferAttribute(mesh.geometry.attributes.position, 0);

Why not save dodecahedron’s geometry awhole (positions, indices etc), plus mesh’s world matrix, and then simply restore that solid from the saved data?

This is the last option if I don’t find a solution. It’s to hard to take several vertices and recreate? For example if i take 4 points in middle i can get position and radius, but the problem is rotation.

Worth to ask it at forums on spatial geometry :slight_smile: