Volume of the Platonic solids
edit on github · preview edits · show history · long url · volume discrete geometry trigonometry elementary geometry algebraic
Numbers
constraint
solid
Volume
$a = 1$
tetrahedron:
0.117851130197757920733474060350808173214139322948079006098056644832561039871842253237532294527303464
$a = 1$
cube:
1
$a = 1$
octahedron:
0.471404520791031682933896241403232692856557291792316024392226579330244159487369012950129178109213857
$a = 1$
dodecahedron:
7.663118960624631968716053920279733412021082129320170017474070179468411619866158573975225214662868981
$a = 1$
icosahedron:
2.181694990624912373503822361971365098100257649838135718446207185587717052349085374756006003491159281
$r = 1$
tetrahedron:
13.85640646055101834821957073204697893554244203048304502444645583561546413527040029664916949405798860
$r = 1$
cube:
8
$r = 1$
octahedron:
6.928203230275509174109785366023489467771221015241522512223227917807732067635200148324584747028994302
$r = 1$
dodecahedron:
5.550291028515510269070432113661839240737598212882498867111753863538836707333245236482938894135950218
$r = 1$
icosahedron:
5.054056143598903991543281911939077361008716607978919166279275578230818425506631590101611767247194759
$\rho = 1$
tetrahedron:
8/3
$\rho = 1$
cube:
2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145
$\rho = 1$
octahedron:
3.771236166328253463471169931225861542852458334338528195137812634641953275898952103601033424873710860
$\rho = 1$
dodecahedron:
3.416407864998738178455042012387657412643710157669154345625383472463125553826829396486486450272693649
$\rho = 1$
icosahedron:
4.120226591665965654697245562437587451468727865371752414236324151368403085459349664714714694595940916
$R = 1$
tetrahedron:
0.513200239279667346230354471557295516131201556684557223127646512430202375380385196172191462742888466
$R = 1$
cube:
1.539600717839002038691063414671886548393604670053671669382939537290607126141155588516574388228665400
$R = 1$
octahedron:
4/3
$R = 1$
dodecahedron:
2.785163863122622967292554912735946987899321772076331992637024147416255150329106493094448513476648088
$R = 1$
icosahedron:
2.536150710120409525643838222345019049081863024335333926526148385147075120227182671250114162588830351
$A = 1$
tetrahedron:
0.051700269950116644385623263721290782652844679204314020838554250615497967444219386808420990061062401
$A = 1$
cube:
0.068041381743977169394369002075163649776831874462685281345352571312526677151592084070551650919573339
$A = 1$
octahedron:
0.073115222941805136712178827877611058620003810566990120929551258810881488622072340725041286124811218
$A = 1$
dodecahedron:
0.081688371824182552180489780788745314462168583253664063449716812175863371880894415608116642314446936
$A = 1$
icosahedron:
0.085604794077281099112044608507108382101970811474244579070359665937969671522693677832147059960628711
Definition
This table lists the volumes of the Platonic solids [1] given that either the edge length $a$ equals $1$, the inner radius $r$ equals $1$, the midradius $\rho$ equals $1$, the outer radius $R$ equals $1$, or the surface area $A$ equals $1$.
Parameters
constraint
—   length that is constrained to be $1$
solid
—   Platonic solid