# Tagged Questions

**6**

votes

**0**answers

83 views

### Does every convex polyhedron have a combinatorially isomorphic counterpart whose angles between edges are rational multiples of $\pi$?

After reading these very interesting questions, I came up with another one:
Does every convex polyhedron have a combinatorially isomorphic counterpart whose angles between all pairs of edges meeting ...

**6**

votes

**0**answers

61 views

### Constructing a polyhedron of maximal possible volume from given bounds on areas of its faces

Consider $n$ variables $a_1,...,a_n$ ranging over $\mathbb{R}^+$. Suppose we are given $n$ pairs of positive rational numbers $(p_1,q_1),...,(p_n,q_n)$ where each pair imposes bounds on the ...

**15**

votes

**1**answer

309 views

### Does every convex polyhedron have a combinatorially isomorphic counterpart whose all faces have rational areas?

Does every convex polyhedron have a combinatorially isomorphic counterpart whose faces all have rational areas?
Does every convex polyhedron have a combinatorially isomorphic counterpart whose edges ...

**3**

votes

**1**answer

254 views

### Grading a non-graded poset as squeezed as possible

Here is a curiosity question (motivated by the recent revamp of ranked-poset routines in Sage).
Let $P$ be a finite poset. We look for a family $\left(a_p\right)_{p\in P}$ of real numbers summing up ...

**13**

votes

**2**answers

1k views

### How many vertices/edges/faces at most for a convex polyhedron that tiles space?

I wonder if this problem has already been examined before:
Consider a convex polyhedron that tiles $\mathbb R^3$. What is the maximum of vertices/edges/faces that such a polyhedron can have?
...

**7**

votes

**3**answers

605 views

### Not quite regular polyhedra

Take a naive interpretation of regular polyhedra:
All vertices (including epsilon ball) congruent
All edges congruent
All faces congruent
We can now find interesting families by removing one ...