Creating a Circle w/ Random parts on each ring?

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1

I’m trying to create a Circle of which each ring going outwards from the centre has a random amount of parts in which still maintaining it’s shape.

I’ve attached a short video of how it currently works.
So upon generation of the attachment, it’ll get a Number between 1 & 5 - If the Number is 3 then it wil generate said beams / attachments shown below.

I’ve opted to use a circle motion as it keeps everything in a linear pattern & wish to continue using it.

Does anyone have any suggestions?

local isRandom = math.random(1, 5)
		if isRandom == 3 then
			local Origin = Vector3.new(0, 0, 0)

			local AT0 = Instance.new("Attachment", Jupiter3["Base"])
			AT0.Name = "AT0"
			--AT0.Visible = true

			local AT1 = Instance.new("Attachment", Jupiter3["Base"])
			AT1.Name = "AT1"
			--	AT1.Visible = true

			local Beam_Clone = script:WaitForChild("Beam"):Clone()
			Beam_Clone.Parent = Jupiter3["Base"]
			Beam_Clone.Attachment0 = AT0
			Beam_Clone.Attachment1 = AT1

			local v1 = Num * ((math.pi * 2) / Parts) 
			local X, Y, Z
			X = Radius * math.sin(v1)
			Y = Radius * math.cos(v1)
			Z = Offset

			local v2 = Vector3.new(X, Y, Z)

			AT0.Position = Origin + v2 - Vector3.new(0, 0, 200)
			AT1.Position = Origin + v2 - Vector3.new(0, 0, 200)
		end