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You have to play with it. You need to look at the individual values, its type and compare the values with the UI. Here is sample how to filter asset values by its ValueType and obtain RGB values of Generic->Color and Self Illumination->Filter Color

 

Sub main
	Dim result As New System.Text.StringBuilder()
	result.AppendLine("AssetValues")
	Dim part As PartDocument = ThisDoc.Document
	For Each oAssetValue As AssetValue In part.ActiveAppearance
		If Not oAssetValue.ValueType = AssetValueTypeEnum.kAssetValueTypeColor Then Continue For

		Dim colorValue As Inventor.ColorAssetValue = oAssetValue
		Dim c As Color = colorValue.Value

		result.AppendFormat("{1}{0}{2}{0}{3}" & vbCrLf, vbTab,
		oAssetValue.DisplayName,
		oAssetValue.Name,
		ColorToString(c)
		)
	Next
	Logger.Debug(result.ToString)

	'Direct access
	Logger.Debug("Generic->Color: {0}", ColorToString(part.ActiveAppearance("generic_diffuse").Value))
	Logger.Debug("Self Illumination->Filter Color: {0}", ColorToString(part.ActiveAppearance("generic_self_illum_filter_map").Value))

End Sub

Function ColorToString(color As Color)
	Return String.Format("[{0}, {1}, {2}]", color.Red, color.Green, color.Blue)
End Function