Roses have a lot of meanings in Utena. They are female symbols; they refer to Dios, the Rose Prince, and therefore to Akio who is the same person; they refer to Anthy through Dios and the roses that she cultivates; they are emblems of the Academy as an institution; spinning rose symbols mark some important events and hint (often confusingly) at their nature by the color of the rose; a single rose can be given as a challenge to a duel; roses can appear in vases or pots or bouquets with varying meanings; the color mix of roses appearing near a character tells us about them, or about the situation. Thorny rose vines in the original prince story and at the Rose Gate refer to the briars of the fairy tale Sleeping Beauty.
For outside meanings that may be brought into Utena’s rose symbolism, I am with Umberto Eco, who wrote “The rose is a symbolic figure so rich in meanings that by now it hardly has any meaning left.” Utena has to draw any outside connections itself.
There are several variations on the rose emblem of Ohtori Academy. I’ll show three of them. The names of Utena and Anthy also refer to roses. The earrings of episode 35 are related.
Early in episode 1, the smell of Anthy’s roses reminds Utena of the prince she met when small. Roses, Dios, check, guy’s probably friends with Tuxedo Mask (Wikipedia) from Sailor Moon. There are roses in the stonework all over the place, so Akio and Anthy must have been around the Academy since long ago. Many of the roses depicted around the school are fully open, but in the emblems that directly represent the Academy, the flowers are still opening. From the official point of view of the Academy, the closed flowers refer to the school’s nominal job of overseeing the students’ maturation. And we onlookers can take that view too, but the flowers also refer to Anthy personally. While the students are immature, she is closed off: She interacts little with others and conceals her feelings. The calyx surrounds and protects the petals as they develop, then opens to allow the flower to open. When Anthy leaves the Academy, its emblems no longer refer to her; she has opened fully. That seems to be the meaning. I hear an echo of the Buddhist symbol of the lotus flower; when fully open, it represents awakening (or as we usually say in English, enlightenment)
Utena’s rose signet. The four outer shapes with the pointy ends are the calyx and refer to Utena. Inside them is a circle of rose petals of a rose that is just opening, referring to Anthy. Together they make a whole flower. The stem and leaf may remind us that there are a few supporting characters around too, and it’s possible that they are a little bit essential!
The petals of the rose can also be read visually as a drawing of the ring itself: The big round petal at the bottom is the opening of the ring, and the diamond or cross shape of the unopened petals is the emblem. Reflected light emphasizes the resemblance. It looks as though the calyx on the signet opened and recursively revealed the signet itself. It’s a reminder that Utena, caught in Akio’s illusions, forgets Anthy in the prince story, and remembers only Dios. It also symbolizes the self-connected nature of the story. I expect to find an Ouroboros reference somewhere!
In this view from episode 1, the body of the ring is tinted purple for corruption, and the pink face of the emblem is shadowed and purple. The ring was given by Akio as part of a corrupt plot. In episode 3, when Utena looks at the ring as evidence of meeting the prince, the ring body is silvery to go with Dios’s white and the emblem is pink for Utena. Looking at objective evidence (which she rarely does early in the series) points to Utena’s future enlightenment.
The emblem on the sign at the school’s entrance, giving the school’s logo and name and whatnot. This variant is a little harder to make out because it’s busier, but the four pointy sepals of the calyx are visible with the circle of petals inside, and the drawing of the ring is still there. The rose over the Student Council entrance matches.
Only an edge of the text is visible in the image. In full, it reads “Private Ohtori Academy Middle School Division/High School Division.” The elementary school is not mentioned on the sign. Maybe the younger kids have a separate entrance?
The green background means that the purpose of the Academy is control.
The dueling arena, seen from above in episode 38, showing the huge planetarium projector and the tiny Utena and Akio. The rose emblem is simplified and includes only the petals, not the calyx: The enchanted forest, though overseen by Ohtori in the form of the large stone bird (Zeus’s eagle and the bird that is to break the shell of the world; see the name Ohtori), is guarded by the entry gate with stone roses outside and living roses inside. It is Anthy’s realm, and its rose emblem indicates Anthy without Utena. As in the others, the petals are opening but not open. Of course, it is also Akio’s realm. One interpretation of the arena emblem is that it shows Akio keeping Anthy closed off and separated from any support. Another interpretation is that it represents the essence of the Academy, its abstract illusionary nature—with the illusion projector at the center.
The emblem is also a reference to Nadia with another meaning.
The floor of the “gondola”, or elevator to the arena, displays a similar emblem.