Table:
0
A
B
C
D
E
1
Name
Vertices V
Edges E
Faces F
Euler characteristic: V − E + F
2
Tetrahedron
4
6
4
2
3
Hexahedron or cube
8
12
6
2
4
Octahedron
6
12
8
2
5
Dodecahedron
20
30
12
2
6
Icosahedron
12
30
20
2

Questions and formulas:
Question: What is the total number of E edges of the polyhedra with vertices V greater than 20?
Formula: SUM(FILTER(C1, B1>20))
Formula2: SUM(FILTER(C2:C6, B2:B6>20))
Level: easy
Question: What is the lowest Euler characteristic: V-E+F of a hexahedron or cube, which has less than 20 faces F, less than 30 edges E, and less than 8 vertices V?
Formula: MIN(FILTER(E1, (D1<20)*(C1<30)*(A1="hexahedron or cube")*(B1<8)))
Formula2: MIN(FILTER(E2:E6, (D2:D6<20)*(C2:C6<30)*(A2:A6="hexahedron or cube")*(B2:B6<8)))
Level: easy