Calvin and Hobbes are both experiencing personal crises at the moment - the former is doing math homework, and the latter is out of tuna. Calvin goes to his parents to tell them to grab some when they go to the store, but when he sees how fancy they're dressed, they reveal they're also going to a movie, which means Rosalyn is coming to babysit. The two panic and get worked up into a frenzy when they see her car pull up in the driveway, and in a moment of desperation, Calvin suggests they hide inside the Hypercube. Although reluctant, Hobbes eventually agrees, and they both dive inside just as Rosalyn enters the house.
The inside of the Hypercube is a swirling white vortex with a mountain of items floating inside it, and most of Calvin's possessions are floating around the portal, which hangs in the sky. Calvin is thrilled when he finds his 10th Anniversary Double-Length Special Edition Captain Napalm issue, but he is forced to leave it behind when he finds that Hobbes has run off in a blind panic. He eventually finds him panicking inside an empty oil drum, and after telling him off, it now transpires that due to the physics of the dimension, they are now potentially miles away from the portal. And now they're both lost.
While Rosalyn is searching the house for Calvin, he and Hobbes wander through the mountains of stuff for their portal, engaging in inane conversation to pass the time. They spent half the story just jumping from topic to topic, from the origins of scotch tape to the structural integrity of Roman cathedrals.
Eventually, they can hear Rosalyn shouting for them, so they head in that direction. However, when they find the portal, they see it going up and down very rapidly, and they can hear Dr Brainstorm grumbling about his storage cube always clogging. Realizing they've made a wrong turn somewhere, they immediately seek out another portal. They find one and end up in some sort of laboratory. Fortunately, they find a second Hypercube and jump inside it, which takes them to another part of the dimension. They keep finding more portals and Hypercubes, allowing them to travel through a desert, a Japanese hut, and then finally, Sherman's lab.
Once there, they remember that the MTM has a hypercube of it's own. While there, they see on a security monitor that Calvin's parents are almost home. Hobbes decides to let Calvin go on ahead, while he takes the MTM back to the house, figuring the two portals will be close together. Calvin makes it inside the vortex, and when he arrives, he sees another portal, and the 10th Anniversary Double-Length Special Edition Captain Napalm issue is floating around it. He passes through the portal, and he ends up back in his room, just as Rosalyn walks in. Although she's angry at him for hiding all night, he points out that he technically hasn't done anything wrong, so he gets off scot-free.
When Hobbes returns that night (having been caught by Sherman), he finds Calvin working on the test from earlier. He welcomes the distraction of getting tuna, so they leave the room, and the Hypercube glows in the dark.
* ConversationalTroping: Lots of it.