The 1976 Standard Atmosphere to 86 kilometers is defined. The data is taken from the official U.S. Government publication.
The equations used are those adopted 15 October 1976 by the United States Committee on Extension to the Standard Atmosphere (COESA), representing 29 U.S. scientific and engineering organizations. The values selected in 1976 are slight modifications of those adopted in 1962. The equations and parameters used are documented in a book entitled U.S. Standard Atmosphere, 1976 published by the U.S. Government Printing Office, Washington, D.C.
h1 and h2 are geopotential altitude in kilometers of the lower and upper boundaries of a layer. The gradient dT/dH is kelvins per kilometer.
Note: 84.852 km geopotential=86 km geometric
These data along with the sea level standard values of
Sea level pressure = 101325 N/m2
Sea level temperature = 288.15 K
Hydrostatic constant = 34.1631947 kelvin/km
define the atmosphere. The sea level density of 1.225 kg/m3 is derived from the fundamental quantities above.
The values of pressure at the boundaries between layers are not an explicit part of the standard because they are derivable from the values of temperature gradient and the hydrostatic equations. If you want to see how the pressures were computed, I have made the computing program and its results available.
You may read the page describing the hydrostatic equations. XHTML+MathML, 12KB or PDF, 69KB.