Classical Geometry Challenges

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2D Shapes

No Shape name Description Solutions
1 Regular Triangle A triangle that has three equal sides and angles.  
2 Right Angle Triangle A triangle that has a right angle.  
3 Isosceles Triangle A triangle that has two equal sides.  
4 Scalene Triangle A triangle that has three sides in different lengths.  
5 Square A 2D shape that has exactly four 90-degree internal angles and four equal sides.  
6 Rectangle Exactly 2 pairs of parallel sides, exactly 4 pairs of adjacent angles are congruent.  
7 Kite At least 2 pairs of adjacent sides are congruent, at least 1 pair of opposite angles is congruent.  
8 Rhombus Exactly 2 pairs of parallel sides, exactly 4 pairs of adjacent sides are congruent, exactly 2 pairs of opposite angles are congruent.  
9 Parallelogram Exactly 2 pairs of parallel sides.  
10 Trapezium At least 1 pair of parallel sides.  
11 Pentagon 5 sided polygon.  
12 Hexagon 6 sided polygon.  
13 Heptagon 7 sided polygon.  
14 Octagon 8 sided polygon.  
15 Nonagon 9 sided polygon.  
16 Decagon 10 sided polygon.  
17 n-gon Need to provide a LOGO procedure that can create n-gon with specified n.  

3D Shapes

No Shape name Description Solutions
1 Cube   /node/121
2 Cylinder    
3 Cone    
4 Sphere    
5 Torus    
6 Triangular Prism    
7 Rectangular Prism    
8 Pentagonal Prism    
9 n-gonal Prism    
10 Anti-Prism    
11 Triangular Pyramid    
12 Rectangular Pyramid    
13 Pentagonal Pyramid    
14 n-gonal Pyramid    

Platonic Solids

No Shape Description Solutions
1 Tetrahedron /node/124
2 Hexahedron /node/121
3 Octahedron /node/125
4 Dodecahedron /node/127
5 Icosahedron /node/94

Archimedean solid

https://en.wikipedia.org/wiki/Archimedean_solid