< drawing a rectangle, select it, do Transform/Rotate, picked the origin as the center point,
Yes I make the same

then typed 45 "On the numeric keyboard of the computer" and push enter
= you arrive in the menu of the Extrusion!!!
So you don't see any rotation but an extrusion in Wip :)
And it's reproductable at any rotation!

This don't arrive when I use your little numeric inside calculator :)
Maybe all keys of my numeric keyboard is like a shortcut to Extrusion?

It's when I enter a number with "5" at any place!
A soon as a 5 is typed ---> Extrusion !

On your little numeric calculator inside the"5" works fine and I have a rotation :)

My Num lock is enable else i can't type any number :)
Seems I have no 5 as shortcut (but when I type 5 at the beginning of programm I arrive also at the Extrusion!
It's not the same for you?
Mystery of the technic :D
It's the E see follow....maybe it's a shortcut installed by an another prog or another person who intercept the E
No such trouble as I can use you mini calculator!)

[Shortcut Keys]
Ctrl+A=script:moi.geometryDatabase.selectAll();
Ctrl+C=CopyClipboard
Ctrl+N=New
Ctrl+O=Open
Ctrl+S=Save
Ctrl+V=Paste
Ctrl+Y=script:moi.command.redo();
Ctrl+Z=script:moi.command.undo();
Delete=Delete
E=Extrude
F1=script:moi.launchHelp();
H=script:moi.geometryDatabase.invertSelection(); moi.geometryDatabase.hide(); moi.geometryDatabase.selectAll();
I=script:moi.geometryDatabase.invertSelection();
R=Rotate
Space=script:var selection = moi.geometryDatabase.getSelectedObjects(); if ( selection.length == 0 ) moi.geometryDatabase.selectAll(); else moi.geometryDatabase.deselectAll();
[Recent Files]

Normaly My key 5 has no short cut installed :)

Complaint
Function "Move object "face to face" (may be not very easy to code but very practical :)
= You clic a face of object one, you clic a face of object two
--> Object one is moving to object two face to face cliked :)

image : More combinaison of blocks

< But then you want it to automatically rotate?
Yes that is the challenge a 3 matrix rotation + Move :)

< You could maybe build a Roman aqueduct with some of those pieces
You don't know Muqarnas ? Mine are free adaptation of it :)
So a Roman aqueduct will be an historical transfiguration scaling :)
http://www.iwr.uni-heidelberg.de/groups/ngg/Muqarnas/basic.php?L=E

A tremendous study of it! http://www.tamabi.ac.jp/idd/shiro/muqarnas/default-.htm
(slide the page if you have some free time :)

< But then you want it to automatically rotate?
Something can help the process :)
3 clicks on a face's object One (a plan defined), 3 clicks for the object Two
Surely more easy to speak than to code :)