Some Geometric Ideas

Object
Number
Object Name dimensions vertices
(points)
edges
(lines)
faces
(planes)
cubes hypercubes   dimensions vertices
(points)
edges
(lines)
faces
(plains)
cubes
  Progression of a dot:             Unfolded:          
1 point 0 1 - - - -   - - - - -
2 line 1 2 1 - - - point 0 2/1 - - -
3 square 2 4 4 1 - - line segments/line 1 5/2 4/1 - -
4 cube 3 8 12 6 1 - flat cross 2 14 19 (6) -
5 hypercube (Tesseract) 4 16 ? 32 ?  24 ? 8 ? 1 8 cubes in a cross 3 36 44 40/29 8
  Other Stuff:                        
  3 sided pyramid (Tetrahedron) 3 4 6 4 - - 4 triangles 2 6 9 (4) -
  4 sided pyramid 3 5 8 5 - - 4 triangles, 1 square 2 8 12 (5) -
  5 sided pyramid 3 6 10 6 - - 5 triangles, 1 pentagon 2 10  15 (6) -
  Octahedron 3 6 12 8/(9) - - 8 triangles 2 10  17 (8) -
  Dodecahedron 3 20 30 12 - - 12 triangles 2 38  49  (12) -
  Icosahedron 3 12 30 20 - - 20 triangles 2 22 31 (20) -

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Neil Rieck
Kitchener - Waterloo - Cambridge, Ontario, Canada.