Surface area of the Platonic solids

constraint

solid

area

$a = 1$

tetrahedron:

1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575

$a = 1$

cube:

6

$a = 1$

octahedron:

3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151

$a = 1$

dodecahedron:

20.64572880706760307310814372866331519288849004012237995048513648428642790650759477598929489665105288

$a = 1$

icosahedron:

8.660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878

$r = 1$

tetrahedron:

41.56921938165305504465871219614093680662732609144913507333936750684639240581120088994750848217396581

$r = 1$

cube:

24

$r = 1$

octahedron:

20.78460969082652752232935609807046840331366304572456753666968375342319620290560044497375424108698290

$r = 1$

dodecahedron:

16.65087308554653080721129634098551772221279463864749660133526159061651012199973570944881668240785065

$r = 1$

icosahedron:

15.16216843079671197462984573581723208302614982393675749883782673469245527651989477030483530174158427

$\rho = 1$

tetrahedron:

13.85640646055101834821957073204697893554244203048304502444645583561546413527040029664916949405798860

$\rho = 1$

cube:

12

$\rho = 1$

octahedron:

13.85640646055101834821957073204697893554244203048304502444645583561546413527040029664916949405798860

$\rho = 1$

dodecahedron:

12.04868495317363679218786035796452853983566764331200087326784824627229472654814420293669360307525122

$\rho = 1$

icosahedron:

13.23169076499214995403073624735217489995494056139551057579847172242315958789421077724151183413072209

$R = 1$

tetrahedron:

4.618802153517006116073190244015659645180814010161015008148818611871821378423466765549723164685996201

$R = 1$

cube:

8

$R = 1$

octahedron:

6.928203230275509174109785366023489467771221015241522512223227917807732067635200148324584747028994302

$R = 1$

dodecahedron:

10.51462224238267212051338169695753214570995864486683563057871046482422292806428036743265257663105141

$R = 1$

icosahedron:

9.574541383273939164915932615493924447762209127520624627382922262292363985214042303772887113855138720

$V = 1$

tetrahedron:

7.205621731056016360052792324097257077790444509355893350110228342695233624114567516268450730218521578

$V = 1$

cube:

6

$V = 1$

octahedron:

5.719105757981619442544453972396562946637442567902081239655857241552507174386170248041811430392081677

$V = 1$

dodecahedron:

5.311613997069083669796666701461086337809888399341493422663761016884993104265681047701440824017902919

$V = 1$

icosahedron:

5.148348556199515646330812946116019064100864116386724148450713675398032479050857713029837325629943109