1
Introduction
2
The Noperthedron
▶
2.1
Definition of the Noperthedron
3
Rupert pairs
▶
3.1
Rupert sets
3.2
Shadows and the separation criterion
4
Cayley coordinates
▶
4.1
Outer views
5
The reduction
▶
5.1
Moves that preserve Rupert pairs
5.2
Step A: the outer view
5.3
Step B: the relative rotation
5.4
Step C: the chart
5.5
The reduced domain
5.6
Blowing up charts 0 and 4
6
Boxes and leaf certificates
▶
6.1
Boxes
6.2
The gap polynomial
6.3
The blow-up
6.4
Gap leaves
6.5
Domain leaves
7
Lower bounds of polynomials
▶
7.1
The coefficient bound
7.2
The Bernstein bound
7.3
Kronecker packing
8
Irrational data
9
The case analysis and the main theorem
▶
9.1
Root boxes
9.2
The tree walk
9.3
The main theorem
10
Bibliography
Dependency graph
Noperthedron
David Renshaw Jason Reed
1
Introduction
2
The Noperthedron
2.1
Definition of the Noperthedron
3
Rupert pairs
3.1
Rupert sets
3.2
Shadows and the separation criterion
4
Cayley coordinates
4.1
Outer views
5
The reduction
5.1
Moves that preserve Rupert pairs
5.2
Step A: the outer view
5.3
Step B: the relative rotation
5.4
Step C: the chart
5.5
The reduced domain
5.6
Blowing up charts 0 and 4
6
Boxes and leaf certificates
6.1
Boxes
6.2
The gap polynomial
6.3
The blow-up
6.4
Gap leaves
6.5
Domain leaves
7
Lower bounds of polynomials
7.1
The coefficient bound
7.2
The Bernstein bound
7.3
Kronecker packing
8
Irrational data
9
The case analysis and the main theorem
9.1
Root boxes
9.2
The tree walk
9.3
The main theorem
10
Bibliography