To reduce the space between actions icons, in your styles.xml you need to create a actionButtonStyle and referencing it your main theme (ex: "AppTheme").
1st step (put the two sentences):
<style name="AppTheme" parent="Theme.AppCompat.Light">
...
<item name="android:actionButtonStyle">@style/myActionButtonStyle</item>
<item name="actionButtonStyle">@style/myActionButtonStyle</item>
...
</style>
2nd step (the parameter "android:width" is the great secret):
<style name="myActionButtonStyle" parent="Widget.AppCompat.ActionButton">
<item name="android:minWidth">30dp</item>
<item name="android:maxWidth">48dp</item>
<item name="android:width">38dp</item>
</style>
enjoy it
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