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Dwarves' Earth Treasures Museum:
Polyhedroid Agates
Pariaba, Brazil, South America
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.    Those agates here may be considered strangest of all agates because of their strong geometric shapes, hence, "polyhedroid agate". They were first found in the clay deposits formed from decomposition of rock matrix, but the source turned out to be short-lived. No one was sure of how those agates were formed since their shapes did not match any crystal structures of various minerals that the agate may had replaced. I have found a plenty of evidences/clues (pictures at the bottom of this page) that those polyhedroid agates may be a form of agate-filled gaps between the large calcite/selenite blades in the cavities (more evidences can be found in John Zehann's Agates book). I found and cut a large thunderegg at Rockhound State Park, Deming, New Mexico, and its cavity is completely filled up with black bladelike calcite crystals with agate filling in the gaps. The shapes of the agate filled gaps are strongly geometric (triangles, trapezoids, and other polyhedroid shapes).
  Most polyhedroid nodules are quartz geodes. Black, gray, white seem to be most common colors of the polyhedroid agates.

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3D picture of this specimen ==>
SLAB, Rare mulit-chambered Polyhedroid Agate,
with calcite(or other minerals) blades between the agates
Its other half was featured in Gem Shop Inc.'s 2009 calendar.
(Larger picture not available)		 It is rare for the agate bands to be not flat/linear.
Rare color combo Large specimens
Bright colors Elusive "perfect triangle", one of most sought shapes
Bluish color, banded Rare to find many polyhedroids in a single specimen
(they tend to fall apart)

Evidence that Polyhedroid Agate filled in between Calcite Bladelike Crystals


Found by Jeffrey A. at Rockhound State Park, Deming, New Mexico
    This specimen I found led me to believe that Polyhedroid Agates may have resulted from filling in the gaps between blade like calcite crystals by silica solutions as indicated by the arrows in the second picture (right one), and the calcite crystals (they left rhomdral crystal impressions on the agate rough surfaces) themselves would eventually decompose leaving the agates in the clay deposits. The calcite crystals growing in random directions would account for the agates' lack of geometric regularity as demonstrated by Polyhedoid agate pictured below. What kind of lava rock that hosted the calcite crystals and agate remains unknown to us even the fact that they were found in the clay bed is "screaming" that they're of rhyolitic origins.
You can see the Polyhedroid Agates for Sale at the Online Agate & Thunderegg Shop