The regular Prism

A regular Prism has a regular polygon as base and vertical edges.

The following elements of a regular prism are calculated if two of them are given:

• Edge a
• Altitude h
• Circumradius r_u
• Inradius r_i
• Volume V
• Base B
• Surface S

Given:
¯¯¯¯¯¯
          Vertices  n = 4
          Volume  V = 1
          Surface  S = 6

Results:
¯¯¯¯¯¯¯
               Edge  a = 1
           Altitude  h = 1
  Circumradius rc = 0,70710678
           Inradius ri = 0,5
              Base  B = 1

Given:
¯¯¯¯¯¯
          Vertices  n = 4
          Volume  V = 1
          Surface  S = 10

1st solution:
¯¯¯¯¯¯¯¯¯¯
               Edge  a = 0,41421356
           Altitude  h = 5,8284272
  Circumradius rc = 0,29289322
           Inradius ri = 0,20710678
              Base  B = 0,17157287

2nd solution:
¯¯¯¯¯¯¯¯¯¯
               Edge  a = 2
           Altitude  h = 0,25
  Circumradius rc = 1,4142136
           Inradius ri = 1
              Base  B = 4

See also: