Questions related to polyhedra and their properties.
3
votes
3answers
212 views
What shape is this?
im doing a question that involves a shape with 8 faces, 10 vertices and 16 edges. Can anyone enlighten me as to what this shape is called?
Many Thanks
4
votes
2answers
252 views
Which unfolding of an icosahedron has the least number of edges to be glued?
Does every unfolding of an icosahedron has the same number of edges to be glued to construct it back to the solid?
If yes, what are those numbers for Platonic solids?
If no, which unfoldings have the ...
16
votes
3answers
2k views
Why are there 12 pentagons and 20 hexagons on a soccer ball?
Edge-attaching many hexagons results in a plane. Edge-attaching pentagons yields a dodecahedron.
Is there some insight into why the alternation of pentagons and hexagons yields an approximated ...
1
vote
1answer
307 views
Find the Polyhedron Enclosed by Multiple Faces
I have two faces ($S_1$ and $S_2$), each bounded by a series of Vertex $V$. These two faces may or may not intersect. In addition to that there are two vertical faces $S_3$ and $S_4$, that connect ...
4
votes
2answers
2k views
Tetrahedron inside a sphere
What's the largest regular tetrahedron (side length x) you can fit inside a sphere with a radius of one?
4
votes
3answers
6k views
Height of a tetrahedron
How do I calculate:
The height of a regular tetrahedron, side length 1.
Just to be completely clear, by height I mean if you placed the shape on a table, how high up would the highest point be from ...
4
votes
1answer
248 views
10
votes
1answer
297 views
What property of certain regular polygons allows them to be faces of the Platonic Solids?
It appears to me that only Triangles, Squares, and Pentagons are able to "tessellate" (is that the proper word in this context?) to become regular 3D convex polytopes.
What property of those regular ...
