I do not know if shittim wood has any spirtual significance, but
it is the Bible name of acacia wood.
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The actual word 'acacia' is not mentioned in the KJV, but a type
of wood called shittim is mentioned. This is the name for two types
of acacia species.
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The word (which first appears in Exodus 25:5) is "shittim," ending with an "M." Most newer translations render it "acacia" (New King James, Standard, NIV).
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The Israelites stayed in Shittim for several days before they crossed the Jordan River, as mentioned in the Bible in Joshua 3:1.
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Isaac - Genesis 22:6
6 And Abraham took the wood of the burnt offering, and laid it upon Isaac his son; and he took the fire in his hand, and a knife; and they went both of them together.