Dating Polyhedra

“Hey, this is interesting! Here’s an article about a sculpture installation that keeps track of the date. We can take a trip out to the desert tomorrow and view it from the road.”
“Ah Mom, I don’t want to go anywhere tomorrow. Besides I can see what date it is on the wall calendar or in the newspaper.”
“Look this is in the Culture category and you need to cultivate that side of you. These are giant glass forms that flip themselves to show the weekday, month and day of the month. For weekdays it’s a seven-sided body…”
“You mean a pentagonal prism?”
“Right, you sure know your geometry. And for the month, there’s a 12-sided…”
“Dodecahedron, and there’s probably some 31-sided polyhedron for the day?”
“No, there are two…for 0-3 a tetrahedron and for 0-9 a…”
“A pentagonal deltohedron. Wow, but how do they move?”
“It says there’re like greenhouses, each absorbs heat from the morning sun that works directly on Nitinol levers to flip them one or two times to angle the correct face forward.”
“That would be like massive ‘muscle wires’, awesome!”
“The polyhedra are completely autonomous, though there’s a computer inside each one.”
“I knew there was a catch.”
“It’s just to tell each block how to turn and to avoid a collision.”
“Cool, let’s get up really early so we can see when they move.”