“The system of 25 great circles of the vector equilibrium defines its own lowest common multiple spherical triangle, whose surface is exactly 1/48th of the entire sphere’s surface. Within each of these 1/48th-sphere triangles and their boundary arcs are contained and repeated each time all of the unique interpatterning relationships of the 25 great circles.”
— R. Buckminster Fuller, Synergetics, 453.01
The Basic Equilibrium LCD Triangle subdivides the surface of the sphere into 48 equal parts and is derived from the 25 great circles of the vector equilibrium. It is one of three spherical triangles on which all geodesic dome calculations are based. The other two are: the basic disequilibrium LCD triangle which subdivides the sphere into 120 equal parts and is derived from the 31 great circles of the icosahedron, and; the 1/24th triangular subdivision of the spherical tetrahedron.
Surface Angles:
BAC=30.0000°; CAD=30.0000°; ABC=90.0000°; ACB≈61.8745°; ACD≈118.1255°; ADC=atan(√2/2)≈35.2644°; EBC=90.0000°; BCF≈118.1255°; BEF≈73.2213°; CFE≈80.4059°; FCD≈61.8745°; CDF=atan(√2/4)≈19,4712°; CFD≈99.5940°; HEG≈73.2213°; EGH≈65.9052°; EHG=45.0000°; EFG≈99.5940°; FEG≈33.5573°; FGE≈48.1897°; GFD≈80.4059°; FDG=atan(√2/2)≈35.2644°; FGD≈65.9052°.
Central Angles:
AB=atan(√2/4)≈19.4712°; AD=atan(√2/2)≈35.2644°; AC≈22.2077°; BC≈10.8934°; CD≈19.1066°; BE≈10.0250°; CF≈6.3532°; EF≈14.4583°; FD≈17.0239°; EG≈19.2863°; FG≈10.6707°; EH≈25.2394°; HG=atan(1/2)≈26.5651°; GD=45-atan(1/2)≈18.4349°; DE≈31.4822°; BD=30.0000°; DH=45.0000°; AH=atan(√2)≈54.7356°.
The Geometry of Thinking 