I know its priceless but what could this rare naturally occuring zirconia go for?
Baddeleyite 1.4ct trillion cut stones.(pictured)
Setting a new minimum for quality inclusion. I give you gem quality Baddeleyite
Faceted Baddeleyite is extremely rare and usually an opaque blue to black. Even if there was a new discovery of surprisingly transparent orange baddeleyite, it would be equally surprising to have them all cut into triangular cushions. But assuming you’ve identified these correctly: the first step in figuring out a value here is to get an identification report from a fully equipped, reputable gem lab. You would also need to know where & when these were discovered. Published article(s) would also help to support your claim. Then, these could be valued by discussions with reputable rare gem dealers who know the collector market.
Thank you. So far on my own they match standard cubic zirconia exactly but show pleocroism. Also brown/yellow are both supported.
Baddeleyite is a rare zirconium oxide mineral (ZrO2 or zirconia), occurring in a variety of monoclinic prismatic crystal forms. It is transparent to translucent, has high indices of refraction, and ranges from colorless to yellow, green, and dark brown.
So not impossible by any stretch. Any ball park though per carrat? Hundreds, thousands, $10,000…etc
So it was identified it is Simpsonite and not Baddeleyite. Sorry if I got anyones hopes up…
I hate to say this…but I must…Simpsonite is in my experience, well the only word that best describes it is, dull. From what I see in your photo those stones are NOT dull. Simpsonite does not have that type of clairity nor shine. Someone must have given you a wrong diagnosis. 
I know I will be slammed for my verbiage but it’s Friday. I had some nice “clear” Simpsonite in college but that was a lifetime ago and heaven only knows where they are now. Trust me they did not have near the shine that your stones have. I hope that you indeed do have Baddeleyite. If not and they are indeed Simpsonite they are quite unique specimens.
All the very best
Otter
Baddeleyite
Crystal Data: Monoclinic. Point Group: 2/m.
Crystals commonly tabular on {100} and somewhat elongated on [010], or short to long prismatic along [001], to 6 cm; rarely equant; prism faces striated ∥ [001]; radially fibrous with concentric banding in botryoidal masses. Twinning: Ubiquitous; on {100} and {110}, both may be polysynthetic; rare on {201}.
Physical Properties:
Cleavage: {001} nearly perfect, {010} and {110} less perfect. Fracture: Subconchoidal to uneven. Tenacity: Brittle. Hardness = 6.5 D(meas.) = 5.40–6.02 D(calc.) = [5.83] Blue-green cathodoluminescence.
Optical Properties: Transparent; in dark-colored specimens, only in thin fragments.
Color: Colorless to yellow, green, greenish or reddish brown, brown, iron-black; colorless to brown in transmitted light.
Streak: White to brownish white.
Luster: Greasy to vitreous; nearly submetallic in black crystals.
Optical Class: Biaxial (–). Pleochroism: X = yellow, reddish brown, oil-green; Y = oil-green, reddish brown; Z = brown, light brown.
Orientation: X ∧ c = 13◦; Y = b. Dispersion: r > v, rather strong. Absorption: X > Y > Z. α = 2.13(1) β = 2.19(1) γ = 2.20(1)
2V(meas.) = 30(1)◦ 2V(calc.) = 28◦
Cell Data: Space Group: P21/c (synthetic). a = 5.1505(1) β = 99.230(1)◦ Z = 4
X-ray Powder Pattern: Phalaborwa, South Africa.
3.15 (10), 2.835 (9), 2.62 (5), 1.817 (5), 3.66 (4), 3.51 (4), 1.847 (4)
b = 5.2116(1)
c = 5.3173(1)
(2)
100.67
Chemistry: (1) (2)
SiO2 0.19 0.08 HfO2 TiO2 0.56 Fe2O3 ZrO2 98.90 97.8 FeO
(1) 0.93 CaO 0.06 LOI 0.28
(1) (2) 0.82
(1) Balangoda, Sri Lanka. (2) Axel Heiberg Island, Canadian Arctic Archipelago; by electron microprobe, average of 35 analyses.
Occurrence: An accessory mineral in carbonatites and kimberlites; in syenites, diabases, gabbros, anorthosites; detrital in gem gravels. In lunar basalt, tektites, and meteorites.
Association: Ilmenite, zirkelite, apatite, magnetite, perovskite (Jacupiranga mine, Brazil); fluorite, nepheline, pyrochlore, allanite (Monte Somma, Italy).
Distribution: At Rakwana and Balangoda, Sri Lanka. From Monte Somma, Campania,
Italy. In Russia, large crystals from the Kovdor massif, and in the Gulinskii massif, the Vuoriyarvi carbonatite complex, and the Imandrovsky layered intrusion, Kola Peninsula; in the Lukkulaisvaara layered intrusion, Karelia. At the Jacupiranga mine, S ̃ao Paulo, and at Po ̧cos de Caldas, Minas Gerais, Brazil. From Bozeman, Gallatin Co., Montana, USA. In the Bingo deposit, Kivu Province, Congo (Zaire). From Catanda, Angola. At Benfontein, and in large crystals from Phalaborwa, Transvaal, South Africa. Other minor occurrences are known.
Name: For Joseph Baddeley, who first called attention to the Sri Lankan material. Type Material: The Natural History Museum, London, England
I would willing to be part with one if you cover shipping to get your diagnosis on these. If you are capable of testing them.
Otter here’s an official picture of simpsonite rough. Looks pretty shiney and similar. Mine’s obviously translucent all 5 test also conclude it is very likely simpsonite. For how rare and desirable it is I don’t see anyone trying to do their own testing. simpsonite10447a|363x327
