1
vote
0answers
13 views

Volume of overlap between two convex polyhedra

I have two convex polyhedra represented by triangle meshes. I can easily determine if they are in contact or not, but when they are in contact then I would like to determine the volume of their ...
1
vote
2answers
68 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
0
votes
0answers
49 views

Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
2
votes
0answers
21 views

The exact type of my 3d model

I have reconstructed vertical features (hole like objects lie on a vertical face) lie on two connected faces. To understand the situation, I say I have 2 walls with many windows and doors on ...
0
votes
1answer
272 views

How do I determine the Tait-Bryan angles (yaw, pitch, and roll) of polyhedron faces to its center?

I'm modeling a pentagonal hexecontrahedron by placing faces and then rotating them. I've determined the center of each face by using the Cartesian coordinates of the vertices of its dual polyhedron ...
2
votes
1answer
355 views

coordinates of icosahedron vertices with variable radius

I was looking on the wikipedia page about icosahedrons and it says that for edge length $a$ the radius of the circumscribed sphere around the icosahedron is given by $r = a \times ...
0
votes
1answer
250 views

Goldberg polyhedra coordinates

I would 3D-print some Goldberg Polyhedra importing in Sketchup, the coordinates provided on these links: 72 faces (2,1) - (coordinates) 132 faces (3,1) - (coordinates) 192 faces (3,2) - ...
12
votes
1answer
601 views

Floret Tessellation of a Sphere

I'm a programmer looking to create a 3D model of a Floret Tessellation of a sphere, like the one in this picture Class III 8,11 floret planar net (source) If anyone could point me in the right ...
2
votes
3answers
1k views

Given a tetrahedron, how to find the outward surface normals for each side?

Say I have a triangle in $3$D space. I can get the surface normal by calculating the vector cross product of two of the edges. But, lets say I make this a tetrahedron. How can I work out the outward ...
1
vote
1answer
332 views

Regular polygons that touching to a sphere surface

What is the possible number of n sided polygons(every face is the same regular polygon) that touching their corners to sphere surface and also touching each other ? I would like to know the relation ...
-1
votes
1answer
759 views

Icosahedron coordinates

Wikipedia says (link)that cartesian coordinates of icosahedron are: (0, ±1, ± φ) (±1, ± φ, 0) (± φ, 0, ±1) Where φ = (1 + √5) / 2 is golden ratio ≈ 1.618. I ...
2
votes
1answer
604 views

How can I determine the radius of a dodecahedron?

I am making a dodecahedron that needs to fit inside of a sphere. The sphere has a diameter of 56mm. What is largest possible measurement of one segment of a pentagon side of a dodecahedron that would ...
2
votes
1answer
185 views

How to determine the intersection of 6 planes?

ABCD is a tetrahedron (not necessarly a regular one). A Monge's plane is a plane which is perpendicular to an edge and goes through the middle of the opposite edge. I want to prove that the 6 ...