Tagged Questions
2
votes
0answers
99 views
Algorithm for Collection of Shortest Paths in a Grid without any clash at a point of time.
The efficient algorithm needs to be done and proved for the best solution for the given problem:
User inputs: (#) Size of the NxN Grid. (N); (#) No. of Paths: Z; (#) Source and Destination ...
6
votes
2answers
263 views
Tiling pythagorean triples with minimal polyominoes
Given a Pythagorean triple $(a,b,c)$ satisfying $a^2+b^2=c^2$, how to calculate the least number of polyominoes of total squares $c^2$, needed, such that both the square $c^2$ can be build by piecing ...
0
votes
1answer
51 views
Determine if two polyhedrals are the same shape and if so, map their vertices
I have a polyhedron and want to determine whether it is combinatorially equivalent to another polyhedron. I know how many faces comprise each polyhedron and for each face, I know all of its vertices, ...
7
votes
2answers
211 views
Number of distinct nets of dual polyhedra
There are 11 non-congruent nets of a cube as well as 11 distinct nets of an octahedron. Both a dodecahedron and an icosahedron have 43380 distinct nets.
Is it true that any pair of dual convex ...
1
vote
0answers
94 views
Complexity of Counting the number of inducing $n$-gons
Definition: A $n$-gon is simple if it has no self intersection and is in general position if no pair of its edges are parallel.
It is clear that by extending the edges of each simple $n$-gon in ...
5
votes
1answer
118 views
How to check if a polytope is a smooth Fano polytope?
Question:
We say that a convex lattice polytope $P\subset \mathbb{R}^d$ is a smooth Fano polytope if:
The origin is contained in the interior of $P$
The vertices of every facet of $P$ are a ...
