<prompt> Pembetatu nane za mshikamano za equilateral, kila moja ya rangi tofauti, hutumiwa kuunda octahedron ya kawaida. Kuna njia ngapi za kutofautisha za kuunda octahedron? Oktahedroni mbili za rangi zinaweza kutofautishwa ikiwa haziwezi kuzungushwa ili zionekane kama nyingine.asy kuagiza tatu; kuagiza hisabati; ukubwa wa kitengo 1.5cm; currentprojectionorthografia2,0.2,1; triple A0,0,1; triple Bsqrt22,sqrt22,0; triple Csqrt22,-sqrt22,0; mara tatu D-sqrt22,-sqrt22,0; triple E-sqrt22,sqrt22,0; mara tatu F0,0,-1; kuchoraA--B--E--mzunguko; kuchoraA--C--D--mzunguko; kuchoraF--C--B--mzunguko; choraF--D--E--cycle,dottedlinewidth0.7; asytextbf A 210 qquad textbf B 560 qquad textbf C 840 qquad textbf D 1260 qquad textbf E 1680  <response>: Kwa kuwa octahedron haiwezi kutofautishwa na mzunguko, bila kupoteza kwa ujumla kurekebisha uso kuwa nyekundu.asy ukubwa8cm; defaultpen 0.5; kuagiza tatu; kuagiza hisabati; currentprojectionorthografia2,0.2,1; triple A0,0,1; triple Bsqrt22,sqrt22,0; triple Csqrt22,-sqrt22,0; mara tatu D-sqrt22,-sqrt22,0; triple E-sqrt22,sqrt22,0; mara tatu F0,0,-1; kuchoraA--B--E--mzunguko; kuchoraA--C--D--mzunguko; kuchoraF--C--B--mzunguko; choraF--D--E--cycle,dottedlinewidth0.7; chorausoA--B--C--mzunguko,rgb1,.6,.6,nolight;asyKuna 7! njia za kupanga rangi saba zilizobaki, lakini bado kuna mizunguko mitatu inayowezekana kuhusu uso uliowekwa, kwa hiyo jibu ni 7!3 1680.asy ukubwa8cm; defaultpen 0.5; kuagiza tatu; kuagiza hisabati; currentprojectionorthografia2,0,1; triple A0,0,1; triple Bsqrt22,sqrt22,0; triple Csqrt22,-sqrt22,0; mara tatu D-sqrt22,-sqrt22,0; triple E-sqrt22,sqrt22,0; mara tatu F0,0,-1; kulia mara tatu0,1,0; picha p picha mpya, r picha mpya, s picha mpya; kuchorap,A--B--E--mzunguko; kuchorap,A--C--D--mzunguko; kuchorap,F--C--B--mzunguko; chorap,F--D--E--mzunguko,upanawa mstari0.7; chorap,usoA--B--C--cycle,rgb1,.6,.6,nolight; chorap,usoA--B--E--cycle,rgb1,1,.6,nolight; ongezamizani32.2p; kuchorar,A--B--E--mzunguko; kuchorar,A--C--D--mzunguko; kuchorar,F--C--B--mzunguko; chorar,F--D--E--mzunguko,upanawa mstari0.7; kuchorar,usoA--B--C--mzunguko,rgb1,.6,.6,nolight; chorar,usoA--C--D--cycle,rgb1,1,.6,nolight; ongezamizani32.2shift2kuliar; kuchoramizunguko,A--B--E--mzunguko; kuchoras,A--C--D--mzunguko; kuchoramizunguko,F--C--B--mzunguko; choramizunguko,F--D--E--mzunguko,upanawa mstari0.7; kuchoras,usoA--B--C--mzunguko,rgb1,.6,.6,nolight; kuchoras,usoB--C--F--cycle,rgb1,1,.6,nolight; ongezamizani32.2shift4kulias; asy 